Chapter.4 Using The Derivative Test Questions & Answers 7e

Applied Calculus, 7e (Hughes-Hallett)

Chapter 4 Using the Derivative

4.1 Local Maxima and Minima

1) The following figure is a graph of a derivative function, . Indicate on the graph the x-values that are critical points and label each as a local maximum, a local minimum, or neither.

Diff: 1 Var: 1

Section: 4.1

Learning Objectives: Identify local extrema of a function given information about its derivative.

2) For which interval(s) is the function f (x) = - 3x decreasing?

A) x < -3 or 3 < x

B) -3 < x < 3

C) -3 < x < 0

D) 0 < x < 3

E) -4 < x < 4

Diff: 1 Var: 1

Section: 4.1

Learning Objectives: Use the derivative to obtain useful information about a graph or function.

3) Sketch a graph of a function such that (x) = 0 at x = 1, (x) > 0 when when

Diff: 1 Var: 1

Section: 4.1

Learning Objectives: Use the derivative to obtain useful information about a graph or function.

4) Find all of the critical points of f (x) = 2 + 18 + 54x. List them from smallest to largest, separated by commas.

Diff: 2 Var: 1

Section: 4.1

Learning Objectives: Find critical points and classify them as local maxima, local minima, or neither using the first and second derivative tests.

5) Find a value of a such that the function f (x) has a critical point at

Diff: 2 Var: 1

Section: 4.1

Learning Objectives: Find critical points and classify them as local maxima, local minima, or neither using the first and second derivative tests.

6) Suppose f has a continuous derivative whose values are given in the following table.

Is x = -2.5 a potential local minimum, local maximum, or neither?

A) local minimum B) neither C) local maximum

Diff: 1 Var: 1

Section: 4.1

Learning Objectives: Identify local extrema of a function given information about its derivative.

7) The following figure represents the function f , with f (x) = sin(x), a > 0 and x ≥ 0.

A. Determine the first two positive x-intercepts of f . Separate them by a comma.

B. What must the value of a be so that = ?

C. If = , calculate .

A. π, 2π

B. 1

C.

Diff: 2 Var: 1

Section: 4.1

Learning Objectives: Use the derivative to obtain useful information about a graph or function.

8) A brick is heated in an oven and taken out to cool off after a certain time. The temperature T of the brick at any time t is given by T = 104 for t ≥ 0, with T in degrees Celsius and t in minutes. What is the temperature the brick will eventually reach?

Diff: 2 Var: 1

Section: 4.1

Learning Objectives: Find critical points and classify them as local maxima, local minima, or neither using the first and second derivative tests.

9) A stone is thrown vertically upward so that its height, measured in feet, after t seconds is given by What is the maximum height of the stone (in feet)?

Diff: 1 Var: 1

Section: 4.1

Learning Objectives: Find critical points and classify them as local maxima, local minima, or neither using the first and second derivative tests.

10) The following is a graph of f (x). Which of the following statements about (x) are true?

Select all that apply.

A) (x) changes sign at , , and .

B) (x) changes sign at and .

C) (x) has a local maximum or minimum at , , and .

D) (x) has a local maximum or minimum at and .

Diff: 1 Var: 1

Section: 4.1

Learning Objectives: Use the derivative to obtain useful information about a graph or function.

11) Given the curve y = a + b + cx + d, with a = 0, find the relation between the parameters a, b, and c that will ensure that the curve has only one turning point.

Diff: 1 Var: 1

Section: 4.1

Learning Objectives: Find critical points and classify them as local maxima, local minima, or neither using the first and second derivative tests.

12) Which of the following is a critical point? Select all that apply.

Diff: 1 Var: 1

Section: 4.1

Learning Objectives: Identify local extrema of a function given information about its derivative.

13) Consider the following graph of a function. Assume the entire graph is shown. How many local maxima does the function have?

Diff: 1 Var: 1

Section: 4.1

Learning Objectives: Identify local extrema of a function given information about its derivative.

14) Given f (x) = + x. Which of the following are critical points of f ?

A) (0, 1) B) (1, 1.37) C) (-1, 1.72) D) none

Diff: 1 Var: 1

Section: 4.1

Learning Objectives: Find critical points and classify them as local maxima, local minima, or neither using the first and second derivative tests.

15) Suppose F(0) = 4 and (x) = 5x - 10. Then F(x) has a local ________ (maximum/minimum) on at x = ________.

Part A: minimum

Part B: 2

Diff: 3 Var: 1

Section: 4.1

Learning Objectives: Use the derivative to obtain useful information about a graph or function.

4.2 Inflection Points

1) Estimate the inflection points of f (x) if the following graph is the graph of

List inflection points in increasing order of x-coordinates; separate each point with a comma.

A. (2.5,-1)

B. (1,1), (4,-3)

C. (0,0), (2,0), (6,0)

Diff: 2 Var: 1

Section: 4.2

Learning Objectives: Find inflection points given a formula or a graph and determine concavity using the second derivative.

2) The graph of the function y = 4 + 12 - 36x - 80 is:

A. increasing and concave up on what interval?

B. increasing and concave down on what interval?

C. decreasing and concave upon what interval?

D. decreasing and concave down on what interval?

A. (1, ∞)

B. (-∞, -3)

C. (-1, 1)

D. (-3, -1)

Diff: 2 Var: 1

Section: 4.2

Learning Objectives: Find inflection points given a formula or a graph and determine concavity using the second derivative.

3) Assume that the polynomial f has exactly one local maximum, two local minima, and two inflection points. What is the largest number of zeros f could have?

Diff: 1 Var: 1

Section: 4.2

Learning Objectives: Use information about the first and second derivatives to analyze a function and to sketch its graph.

4) Sketch the curve y = 8.

Diff: 1 Var: 1

Section: 4.2

Learning Objectives: Use information about the first and second derivatives to analyze a function and to sketch its graph.

5) If f (x) = cos x for 0 ≤ x ≤ 2π, what is(x)?

A) 2 sin x B) sin x

C) cos x + sin x D) - cos x - sin x

Diff: 2 Var: 1

Section: 4.2

Learning Objectives: Find inflection points given a formula or a graph and determine concavity using the second derivative.

6) If f (x) = cos x for 0 ≤ x ≤ 2π, which of the following are inflection points of

A) 0 B) C) D) π E)

Diff: 1 Var: 1

Section: 4.2

Learning Objectives: Find inflection points given a formula or a graph and determine concavity using the second derivative.

7) Given f (x) = + x. Which of the following are inflection points of f ?

A) (-1, 1.72) B) (0, 1) C) (1, 1.37) D) none

Diff: 1 Var: 1

Section: 4.2

Learning Objectives: Find inflection points given a formula or a graph and determine concavity using the second derivative.

8) For f (x) = cos(2x), determine if is an inflection point.

Diff: 1 Var: 1

Section: 4.2

Learning Objectives: Find inflection points given a formula or a graph and determine concavity using the second derivative.

4.3 Global Maxima and Minima

1) If f (x) = cos x for 0 ≤ x ≤ 2π, which of the following are local and/or global extrema of Select all that apply.

A) 0

B)

C)

D)

E)

F) π

G)

Diff: 1 Var: 1

Section: 4.3

Learning Objectives: Find global extrema of a continuous function defined on a closed interval.

2) f (x) is a function with local minima at x = -4 and x = 6, with x = -4 also a global minimum; a local maximum at but no global maximum; and inflection points at and Could f (x) be of the form

ax6 + bx5 + cx2 + d ?

Diff: 1 Var: 1

Section: 4.3

Learning Objectives: Find global extrema of a continuous function defined on an open interval or on the entire real line.

3) The point x = 1 on the following closed graph corresponds to

A) a local minimum

B) a local maximum

C) neither a maximum nor a minimum

D) a local and global minimum

E) a local and global maximum

Diff: 1 Var: 1

Section: 4.3

Learning Objectives: Find global extrema of a continuous function defined on a closed interval.

4) For + and -1.5 ≤ x ≤ 2.5, find the value(s) of x for which

A. f (x) has a local minimum.

B. f (x) has a local maximum.

C. f (x) has a global minimum.

D. f (x) has a global maximum.

List the value(s) from smallest to largest, separated by commas.

A. -1.5, 2.5

B. 0

C. 2.5

D. 0

Diff: 1 Var: 1

Section: 4.3

Learning Objectives: Find global extrema of a continuous function defined on a closed interval.

5) The distance, s, traveled by a runner in a 20 mile race is given in the following figure, where time, t, is in hours. At which of the following values of t is the runner's speed the slowest?

A) 4 B) 3 C) 1 D) 2

Diff: 2 Var: 1

Section: 4.3

Learning Objectives: Find global extrema of a continuous function defined on a closed interval.

6) For f (x) = 4 x - sin x and 0 ≤ x ≤ π, which of the following statements are true? Select all that apply.

A) f (x) has global maxima at x = 0 and x = π

B) f (x) has global minima at x = 0 and x = π

C) f (x) has global maximum at x =

D) f (x) has global minimum at x =

Diff: 1 Var: 1

Section: 4.3

Learning Objectives: Find global extrema of a continuous function defined on a closed interval.

7) The quantity of a medication in the bloodstream t hours after it is ingested is given, in mg, by What is the maximum quantity of the medication in the bloodstream?

A) 55 mg B) 150 mg C) 408 mg D) 75 mg

Diff: 2 Var: 1

Section: 4.3

Learning Objectives: Find global extrema of a continuous function defined on an open interval or on the entire real line.

8) Daily production levels in a plant can be modeled by the function which gives units produced at t, the number of hours since the factory opened at 8 a.m. Factory productivity is at a maximum at _____ a.m.

Diff: 2 Var: 1

Section: 4.3

Learning Objectives: Find global extrema of a continuous function defined on an open interval or on the entire real line.

9) The number of plants in a terrarium is given by the function P(c) = -1.4 + 3c + 4, where c is the number of mg of plant food added to the terrarium. The amount of plant food that produces the highest number of plants is _____ mg (round to the nearest hundredth).

Diff: 2 Var: 1

Section: 4.3

Learning Objectives: Find global extrema of a continuous function defined on an open interval or on the entire real line.

10) The function y = 0.2 - 8x + 2 gives the population of a town (in 1000's of people) at time x where x is the number of years since 1990. The population was a minimum in the year ________.

Diff: 2 Var: 1

Section: 4.3

Learning Objectives: Find global extrema of a continuous function defined on an open interval or on the entire real line.

11) A normal distribution in statistics is modeled by the function N(x) = . Determine where the maximum value of the function would occur.

A) -4 B) -3 C) 0 D) -4π E)

Diff: 3 Var: 1

Section: 4.3

Learning Objectives: Find global extrema of a continuous function defined on an open interval or on the entire real line.

12) In the function y = 11sin (x) + 4, in the interval from 0 ≤ x ≤ π, at which value(s) of x does the function contain a global maximum?

A) π and

B) 0 and

C) only

D) 6π

E) 3π

Diff: 1 Var: 1

Section: 4.3

Learning Objectives: Find global extrema of a continuous function defined on a closed interval.

13) On the following graph, the point (7, 3) is a

A) local minimum

B) local and global maximum

C) local maximum

D) inflection point

E) local and global minimum

Diff: 1 Var: 1

Section: 4.3

Learning Objectives: Find global extrema of a continuous function defined on a closed interval.

4.4 Profit, Cost, and Revenue

1) The following table shows cost and revenue for a product (in dollars).

A. What is the price of the product?

B. At what value of q is profit is maximized?

A. $0.50

B. 3000

Diff: 1 Var: 1

Section: 4.4

Learning Objectives: Find maximum profit.

2) With x people aboard, a South African airline makes a profit of (1100 - 5x) rands per person for a specific flight. How many people would the airline prefer to have on board?

Diff: 2 Var: 1

Section: 4.4

Learning Objectives: Find maximum profit.

3) Given the following table of production quantities with their corresponding marginal revenue and marginal cost, estimate the production level that maximizes profit.

Diff: 1 Var: 1

Section: 4.4

Learning Objectives: Find maximum profit.

4) If the total revenue and total cost (in dollars) are given by

R(x) = 4x - 0.002

C(x) = 300 + 1.3x?

What quantity of gadgets, to the nearest whole number should be produced to maximize profit? What is the maximum profit?

Diff: 2 Var: 1

Section: 4.4

Learning Objectives: Find maximum profit.

5) What quantity of gadgets should be produced to maximize profit if they sell for $400 per unit and the total cost (in dollars) of producing x units is given by C(x) = 11,500 + 2? What is that profit?

Diff: 2 Var: 1

Section: 4.4

Learning Objectives: Find maximum profit.

6) Total cost and revenue are approximated by the functions C = 1800 + 3.6q and R = 4q, both in dollars.

A. What is the fixed cost?

B. What is the profit function?

A. $1800

B. 0.4q - 1800

Diff: 2 Var: 1

Section: 4.4

Learning Objectives: Find maximum profit.

7) Write a formula for total cost, C, as a function of quantity r when fixed costs are $70,000 and and variable costs are $2600 per item.

Diff: 1 Var: 1

Section: 4.4

Learning Objectives: Find maximum profit.

8) The revenue for selling q items is R(q) = 350q - 3 and the total cost is C(q) = 110 + 50q.

A. Write a function that gives total profit earned.

B. Find the quantity that maximizes profit.

A. 300q- 3 - 110

B. 50

Diff: 2 Var: 1

Section: 4.4

Learning Objectives: Find maximum profit.

9) The function C(r) = 18 - 40 gives cost in dollars of producing r items. What is the marginal cost of increasing r by 1 item from the current production level of r = 5?

Diff: 2 Var: 1

Section: 4.4

Learning Objectives: Find maximum revenue using the demand equation.

10) A. Find the marginal cost for q = 110 when the fixed costs in dollars are 3500, the variable costs are 250 per item, and each sells for $550.

B. Find the marginal revenue under the same conditions.

A. $250

B. $550

Diff: 1 Var: 1

Section: 4.4

Learning Objectives: Find maximum revenue using the demand equation.

11) Let C(q) represent the cost, R(q), the revenue and π?(q) the profit, in dollars of producing q items. If (89) = 79 and (89) = 81 approximately, how much profit is earned by the item?

Hint: (q) = (q) - (q)

Diff: 2 Var: 1

Section: 4.4

Learning Objectives: Find maximum revenue using the demand equation.

12) The total revenue, R, in dollars,when selling q items is R(q) = ln. Calculate and interpret the marginal revenue if

Diff: 2 Var: 1

Section: 4.4

Learning Objectives: Find maximum revenue using the demand equation.

13) The total cost, C, in dollars,when producing q items is Calculate and interpret the marginal cost if

Diff: 2 Var: 1

Section: 4.4

Learning Objectives: Find maximum revenue using the demand equation.

14) The Revenue is given by R(q) = 230q and the Cost is given by C(q) = 2800 + 4.6. What value of q will maximize profit? What is the profit at that value?

q = _____, P(q) = _____

Diff: 2 Var: 1

Section: 4.4

Learning Objectives: Find maximum profit.

15) The total revenue and cost curves for a product are shown in the following figure. Estimate the production level P that maximizes profit.

A) 50 B) 100 C) 150 D) 200

Diff: 1 Var: 1

Section: 4.4

Learning Objectives: Find maximum profit.

16) The total revenue and cost curves for a product are shown in the first figure. Does the second figure accurately show the corresponding marginal cost and marginal revenue functions?

Diff: 2 Var: 1

Section: 4.4

Learning Objectives: Find maximum profit.

17) A water park finds that at an admission price of $12, attendance is 400 per day. For every $1 decrease in price, 40 more people visit the park per day. How many dollars should the park charge for admission to maximize revenue (to the nearest dollar)?

Diff: 1 Var: 1

Section: 4.4

Learning Objectives: Find maximum revenue using the demand equation.

4.5 Average Cost

1) The cost of producing q items is C(q) = 900 + 7q dollars. What is the marginal cost of producing the item?

Diff: 1 Var: 1

Section: 4.5

Learning Objectives: Find minimum average cost.

2) A factory produces a product that sells for $9. They currently produce 2400 items per month, at an average cost of $3 per item. The marginal cost at this level is $4. Assume that the factory can sell all the items that it produces.

A. What is the profit at this production level?

B. Would increasing production increase or decrease average cost?

A. $14,400

B. increase

Diff: 2 Var: 1

Section: 4.5

Learning Objectives: Find minimum average cost.

3) The graph of a cost function is given in the following figure. Estimate the value of q at which average cost is minimized.

Diff: 1 Var: 1

Section: 4.5

Learning Objectives: Visualize average cost on the total cost.

4) 400 items are produced at an average cost of $70 per item. Find the cost of producing the item if the marginal cost to produce the item is $80.

Diff: 2 Var: 1

Section: 4.5

Learning Objectives: Find minimum average cost.

5) You sell hot dogs at a baseball game for $2.75 each. You have 50 hot dogs to sell at an average cost to you of $2.00 each. The marginal cost at is $1.90. Assume you can always sell out of hot dogs. Will increasing the number of hot dogs you have to sell increase or decrease the average cost?

A) decrease B) increase

Diff: 3 Var: 1

Section: 4.5

Learning Objectives: Find minimum average cost.

6) You sell hot dogs at a baseball game for $3.50 each. You have 200 hot dogs to sell at an average cost to you of $3.00 each. The marginal cost at is $3.10. Assume you can always sell out of hot dogs. Will increasing the number of hotdogs you have to sell increase or decrease your profit?

A) decrease B) increase

Diff: 3 Var: 1

Section: 4.5

Learning Objectives: Find minimum average cost.

7) Which average cost function corresponds to the total cost function shown in the following figure?

A)

B)

C)

D)

Diff: 1 Var: 1

Section: 4.5

Learning Objectives: Visualize average cost on the total cost.

8) The average cost per item to produce q items is given by a(q) = 0.2 - 4q + 7.

A. What is the total cost, C(q), of producing q items?

B. What is the marginal cost, MC, of producing q items?

C. At what production level does marginal cost equal average cost?

A. 0.2 - 4 + 7q

B. 0.6 - 8q + 7

C. 10

Diff: 2 Var: 1

Section: 4.5

Learning Objectives: Find minimum average cost.

9) The cost function, in dollars, is C(q) = 4000 + 30q. The average cost of producing 140 units is .

Diff: 2 Var: 1

Section: 4.5

Learning Objectives: Find minimum average cost.

10) The cost function is C(q) = 9,000 + 4.5. For the unit, find the marginal cost and average cost, identify the units.

Diff: 2 Var: 1

Section: 4.5

Learning Objectives: Find minimum average cost.

11) Given the cost function C(q) = 3000 + 10q + 0.005 and the demand function find the value of q (to the nearest whole number) for which revenue is a maximum.

Diff: 2 Var: 1

Section: 4.5

Learning Objectives: Find minimum average cost.

12) The average cost per item to produce q items is given by for What is the total cost, C, of producing q goods?

A) 0.4 - 0.8 + 13q B) 0.4q - 0.8 +

C) 0.8q - 0.8 D) 1.2 - 1.6q + 13

Diff: 2 Var: 1

Section: 4.5

Learning Objectives: Find minimum average cost.

13) The average cost per item to produce q items is given by for What is the marginal cost, MC, of producing q goods?

A) 0.2 - 0.3 + 16q B) 0.2q - 0.3 +

C) 0.4q - 0.3 D) 0.6 - 0.6q + 16

Diff: 2 Var: 1

Section: 4.5

Learning Objectives: Find minimum average cost.

14) The average cost per item to produce q items is given by for At what point q (to two decimal places) does marginal cost equal average cost?

Diff: 2 Var: 1

Section: 4.5

Learning Objectives: Find minimum average cost.

4.6 Elasticity of Demand

1) The elasticity for a good is E = 1.6. What is the effect on demand of a 3% price increase?

A) 4.8% decrease B) 4.8% increase

C) 1.9% decrease D) 1.9% increase

Diff: 1 Var: 1

Section: 4.6

Learning Objectives: Calculate elasticity of demand and understand its interpretation.

2) There is only one barber in a small town. Would you expect the price of a haircut to be elastic or inelastic?

Diff: 1 Var: 1

Section: 4.6

Learning Objectives: Calculate elasticity of demand and understand its interpretation.

3) The demand curve for a product is q = 1500 - 4.

A. Find the elasticity of demand (to three decimal places) at a price of p = 7.

B. Is demand elastic or inelastic at this price?

A. 0.301

B. inelastic

Diff: 2 Var: 1

Section: 4.6

Learning Objectives: Calculate elasticity of demand and understand its interpretation.

4) An amusement park finds that when it charges $23 for an all-day pass, attendance is about 3100 per day. When it charges $26, attendance is about 3100 per day.

A. Estimate the elasticity for the amusement park to two decimal places.

B. Is demand elastic or inelastic?

A. 0.00

B. elastic

Diff: 2 Var: 1

Section: 4.6

Learning Objectives: Calculate elasticity of demand and understand its interpretation.

5) An amusement park finds that when it charges $15 for an all-day pass, attendance is about 3300 per day. When it charges $19, attendance is about 2700 per day. Is daily revenue higher at a price of $15 or a price of $19?

Diff: 2 Var: 1

Section: 4.6

Learning Objectives: Understand the relationship between elasticity and revenue.

6) A youth group wishes to hold a car wash as a fundraiser. Through past experience with car washes, they have constructed the following table, which shows the price, p, charged for a car wash and the quantity, q, of cars washed at that price.

A. At what price is revenue maximized?

B. What is the elasticity at that price?

A. $3.00

B. 0.95

Diff: 1 Var: 1

Section: 4.6

Learning Objectives: Understand the relationship between elasticity and revenue.

7) The demand equation for a product is q = , where q is the number of units produced, p is the price of each unit, and a and b are positive constants. Find a formula, in terms of p, for the elasticity of demand.

Diff: 3 Var: 1

Section: 4.6

Learning Objectives: Calculate elasticity of demand and understand its interpretation.

8) The demand equation for a product is q = , where q is the number of units produced, p is the price of each unit, and a and b are positive constants. Find the critical point(s) of the revenue function.

Diff: 2 Var: 1

Section: 4.6

Learning Objectives: Understand the relationship between elasticity and revenue.

9) The demand for doughnuts at a bakery is given by q = 450 - 275p, where q is the number of doughnuts sold at a price of p dollars each.

A. Find the elasticity of demand to two decimal places if the price is $0.89.

B. Will revenue be increased by raising or lowering the price?

A. 1.19

B. lowering

Diff: 2 Var: 1

Section: 4.6

Learning Objectives: Understand the relationship between elasticity and revenue.

10) Raising the average price of an entree at a restaurant from $8 to $11 reduces the number of customers per day from 325 to 300.

A. What is the elasticity of demand to two decimal places for entrees at a price of $8?

B. Would raising the price from $8 to $11 increase or decrease the profit?

A. 0.21

B. increase

Diff: 2 Var: 1

Section: 4.6

Learning Objectives: Calculate elasticity of demand and understand its interpretation.

11) The demand curve for a product is given by q = 2400 - 6.

A. Write revenue as a function of price and take its derivative to find the price (to the nearest cent) that will maximize revenue.

B. Find the elasticity (to two decimal places) at the price you found in part A.

A. $11.55

B. 1.00

Diff: 2 Var: 1

Section: 4.6

Learning Objectives: Understand the relationship between elasticity and revenue.

12) Rank the following products from 1 to 4 according to their elasticity, with 1 being the highest.

A. high performance automobile

B. cellular phone

C. laundry detergent

D. movie theater tickets

A. 1

B. 3

C. 4

D. 2

Diff: 1 Var: 1

Section: 4.6

Learning Objectives: Calculate elasticity of demand and understand its interpretation.

4.7 Logistic Growth

1) A disease is released into a small town. The number of people infected is modeled by the equation What is the % growth rate of this disease?

Diff: 2 Var: 1

Section: 4.7

Learning Objectives: Understand the key aspects of logistic growth including the effect of the parameters in the formula for logistic growth.

2) A disease is released into a town. The number of people, in thousands infected is modeled by the equation How many people are infected after 0 hours?

Diff: 2 Var: 1

Section: 4.7

Learning Objectives: Understand the key aspects of logistic growth including the effect of the parameters in the formula for logistic growth.

3) A disease is released into a town. The number of people infected each day is modeled by the equation Estimate when Estimate the value of n at this time.

Diff: 2 Var: 1

Section: 4.7

Learning Objectives: Estimate maximum value or maximum growth from a logistic formula or graph or table.

4) The rabbit population, P, in a wilderness area is approximated by the function

P = ,

where t is the number of weeks since the rabbits were introduced into the area.

A. How many rabbits were initially introduced into the area (to the nearest rabbit)?

B. How many rabbits were in the area after 8 weeks (to the nearest rabbit)?

C. What is the carrying capacity of rabbits in the area?

A. 63

B. 456

C. 950

Diff: 3 Var: 1

Section: 4.7

Learning Objectives: Understand the key aspects of logistic growth including the effect of the parameters in the formula for logistic growth.

5) A biologist found that the number of Drosophila fruit flies, N(t), assumes the following growth pattern if the food source is limited:

N(t) = ,

A. How many fruit flies were there in the beginning (to the nearest fly)?

B. At what time was the population increasing most rapidly (to the nearest day)?

C. At what rate does the number of fruit flies increase after 3 days (to the nearest fly per day)?

A. 10

B. 9

C. 12

Diff: 2 Var: 1

Section: 4.7

Learning Objectives: Estimate maximum value or maximum growth from a logistic formula or graph or table.

6) The following table gives the number of students who have joined a new school club t days after it was formed.

A. Estimate the value of t where concavity changes in this function.

B. Use your answer from part (a) to estimate the maximum membership in the club.

A. 8

B. 610

Diff: 1 Var: 1

Section: 4.7

Learning Objectives: Estimate maximum value or maximum growth from a logistic formula or graph or table.

7) The following table shows the total sales, in thousands, since a new DVD was released.

A. Estimate the point of diminishing returns.

B. Using your answer from part (A), predict the total possible sales for the DVD.

A. 501,000

B. 1,002,000

Diff: 1 Var: 1

Section: 4.7

Learning Objectives: Estimate maximum value or maximum growth from a logistic formula or graph or table.

8) The dose response curve in the following figure is given by R = f (x), where R is percent of maximum response and x is the dose of the drug in mg. The inflection point is at (10, 30) and Would f (x) be greater or less than 8 for values of x less than 10?

Diff: 2 Var: 1

Section: 4.7

Learning Objectives: Interpret a dose-response curve.

9) In Wilson corners, population 2000, a rumor spreads according to the logistic model. If 9 people know the rumor at 4 PM and 180 people have heard it by 5 PM, how many people will have heard the rumor by 6 PM (to the nearest person)?

Diff: 2 Var: 1

Section: 4.7

Learning Objectives: Estimate maximum value or maximum growth from a logistic formula or graph or table.

10) A flu epidemic spreads amongst a group of people according to the formula

P(t) = ,

where P(t) represents the number of people that are infected by the end of day t.

A. How many people are infected by the end of the fifth day (to the nearest person)?

B. At what rate do the people become infected on day 5 (to the nearest person per day)?

A. 215

B. 135

Diff: 2 Var: 1

Section: 4.7

Learning Objectives: Estimate maximum value or maximum growth from a logistic formula or graph or table.

11) The drug concentration curve for a drug after t hours is given by The minimum effective concentration is Is the drug effective at hours?

Diff: 2 Var: 1

Section: 4.7

Learning Objectives: Interpret a dose-response curve.

12) The peak concentration of 9 ng/ml for a drug occurs 1.5 hours after a 7 mg dose is administered. Sketch a graph that represents the concentration, C, as a function of time, t.

Diff: 1 Var: 1

Section: 4.7

Learning Objectives: Interpret a dose-response curve.

13) Suppose the spread of a cold virus in an elementary school can by modeled by the equation where P is the number of children with the virus and t is time in days.

A. How many children will eventually catch the virus?

B. At the inflection point of the graph of P, how many children have caught the virus?

C. If a different strain of the virus is found to fit the equation will it eventually infect (1) more children, (2) fewer children, or (3) the same number of children?

A. 80

B. 40

C. 3

Diff: 3 Var: 1

Section: 4.7

Learning Objectives: Understand the key aspects of logistic growth including the effect of the parameters in the formula for logistic growth.

4.8 The Surge Function and Drug Concentration

1) The following three equations are graphed in the figure. Which graph corresponds to equation A?

Diff: 1 Var: 1

Section: 4.8

Learning Objectives: Understand the surge function and the effect of the parameters in the surge function.

2) Does the maximum value of the surge function y = increase or decrease when a is held constant and b is increased?

Diff: 1 Var: 1

Section: 4.8

Learning Objectives: Understand the surge function and the effect of the parameters in the surge function.

3) If time, t, is in hours, and concentration, C, is in ng/ml, the drug concentration curve for a drug is given by About how many hours does it take for the drug to reach peak concentration?

A) 5.0 hours B) 8.1 hours C) 0.2 hours D) 1.6 hours

Diff: 2 Var: 1

Section: 4.8

Learning Objectives: Understand the surge function and the effect of the parameters in the surge function.

4) If time, t, is in hours and concentration, C, is in ng/ml, the drug concentration curve for a drug is given by What is the peak concentration of the drug?

A) 9.9 mg B) 8.1 mg C) 2.4 mg D) 27.0 mg

Diff: 2 Var: 1

Section: 4.8

Learning Objectives: Understand the surge function and the effect of the parameters in the surge function.

5) If time, t, is in hours and concentration, C, is in ng/ml, the drug concentration curve for a drug is given by Suppose scientists wish to alter the drug so that it is effective for more hours. Would the coefficient of 8.8 in its concentration curve equation increase or decrease?

A) increase B) decrease

Diff: 2 Var: 1

Section: 4.8

Learning Objectives: Understand the surge function and the effect of the parameters in the surge function.

6) The following table gives the concentration C, of a drug in ng/ml, at time t, in hours, after it is administered to 2 different people.

A. If the concentration for Person A is given by and the concentration for Person B is given by would you expect to be larger or smaller than ?

B. If the minimum effective concentration is 5 ng/ml, until what time is the drug effective for person A?

C. If the minimum effective concentration is 5 ng/ml, until what time is the drug effective for person B?

A. larger

B. 3

C. 4

Diff: 2 Var: 1

Section: 4.8

Learning Objectives: Understand the surge function and the effect of the parameters in the surge function.

7) The size of a bacteria colony that doubles every 13 hours (as a function of time) is most likely to be modeled by which of the following types of functions?

A) exponential

B) surge

C) logistic

D) periodic

E) linear

Diff: 1 Var: 1

Section: 4.8

Learning Objectives: Understand the surge function and the effect of the parameters in the surge function.

8) Classify the following graph as a probable logistic, polynomial, or surge function.

A) logistic B) polynomial C) surge

Diff: 2 Var: 1

Section: 4.8

Learning Objectives: Understand the surge function and the effect of the parameters in the surge function.

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