Exam Questions 5th Edition Ch.3 Functions And Their Graphs - Test Bank | College Algebra 5e by Young by Cynthia Y. Young. DOCX document preview.
College Algebra, 5e (Young)
Chapter 3 Functions and Their Graphs
3.6 Modeling Functions Using Variation
1) Write an equation that describes the variation. Use k as the constant of variation.
V is directly proportional to 
.
Diff: 2 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develope equation for direct or inverse variation
2) Write an equation that describes the variation. Use k as the constant of variation.
A varies directly with both 
and 
.
Diff: 2 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using direct variation.
3) Write an equation that describes the variation. Use k as the constant of variation.
f varies inversely with both 
and 
.
Diff: 2 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using inverse variation.
4) Write an equation that describes the variation.
s varies directly with the cube of T. s = 84,375 when T = 15.
Diff: 2 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develope equation for direct or inverse variation
5) Write an equation that describes the variation.
V varies directly with m and inversely with q. V = 130 when m = 35 and q = 25.
Diff: 2 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using direct variation.
6) Write an equation that describes the variation.
s varies inversely with both x and the square root of q. s = 47 when x = 18 and q = 1.
Diff: 2 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using inverse variation.
7) Write an equation that describes the variation.
z varies directly with the square root of x and inversely with the cube of u. 
when 
and 
Diff: 2 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using direct variation.
8) Write an equation that describes the variation.
P varies directly with the square root of x and inversely with the cube of u. 
when 
and 
A) P = 
B) P = 
C) P = 
D) P = 
Diff: 2 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using direct variation.
9) A force of 102 N will stretch the spring 17 cm. How far will a force of 120 N stretch the spring?
Diff: 2 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using direct variation.
10) A gas contained in a 30 mL container at a temperature of 200 K has a pressure of 1,600 atm. If the temperature increases to 210 K, what is the resulting pressure?
Diff: 2 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using joint variation.
11) Hooke's Law in physics states that if a spring at rest (equilibrium position ) has a weight attached to it, then the distance the spring stretches is directly proportional to the force (weight).
F = kx
where F is the force in Newtons(N), x is the distance stretched in meters (m), and k is the spring constant (N/m).
A force of 300 N will stretch the spring 20 cm. How much force is required to stretch the spring 
Diff: 2 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using direct variation.
12) A gas contained in a 2 mL container at a temperature of 320 K has a pressure of 1.5 atm. If the container changes to a volume of 1 mL, what is the resulting pressure?
Diff: 2 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using joint variation
13) Levi's makes jeans in a variety of price ranges for juniors. The Silver Tab Baggy jeans sell for about $37, whereas the Offender jeans sell for $150. The demand for Levi's jeans is inversely proportional to the price. If 235,000 pairs of the Silver Tab Baggy jeans were bought, approximately how many of the Offender were bought? Round to the nearest integer.
Diff: 2 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using inverse variation.
14) In physics, the inverse square law states that any physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity. In particular, the intensity of light radiating from a point source is inversely proportional to the square of the distance from the source. Below is a table of average distances from the Sun:
Planet | Distance to the Sun |
Mercury | 58,000 km |
Earth | 150,000 km |
Mars | 228,000 km |
The solar radiation on the Earth is approximately 1,250 watts per square meter. How much solar radiation is there on Mercury? Round to the nearest hundredth watts per square meter.
Diff: 2 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using inverse variation.
15) Write an equation that describes the variation. Use k as the constant of variation.
V is directly proportional to 
.
A) V = 
B) V = ka
C) V = 
D) V = k
Diff: 1 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using direct variation.
16) Write an equation that describes the variation. Use k as the constant of variation.
V varies directly with the cube of z.
A) V = k
B) V = kz
C) V = 
D) V = 
Diff: 1 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using direct variation.
17) Write an equation that describes the variation. Use k as the constant of variation.
f is inversely proportional to 
.
A) f = kb
B) f = 
C) f = 
D) f = k
Diff: 1 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using inverse variation.
18) Write an equation that describes the variation. Use k as the constant of variation.
P varies inversely with the square of h.
A) P = 
B) P = 
C) P = kh
D) P = k
Diff: 1 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using inverse variation.
19) Write an equation that describes the variation. Use k as the constant of variation.
P is directly proportional to both 
and 
.
A) P = kh
B) P = k
C) P = 
D) P = 
Diff: 1 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using direct variation.
20) Write an equation that describes the variation. Use k as the constant of variation.
P is inversely proportional to both and 
.
A) P = 
B) P = 
C) P = k
D) P = 
Diff: 1 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using inverse variation.
21) Write an equation that describes the variation.
A is directly proportional to the cube of L. A = 2 when L = 1.
A) A = 
B) A = 2L
C) A = 2
D) A = 
Diff: 1 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using direct variation.
22) Write an equation that describes the variation.
f is inversely proportional to the square of t. f = 8 when t = 1.
A) f = 
B) f = 
C) f = 8
D) f = 8t
Diff: 1 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using inverse variation.
23) Write an equation that describes the variation. Use k as the constant of variation.
V varies is directly proportional to both 
and . V = 32 when x = 1 and t = 4.
A) V = 
B) V = 2x
C) V = 
D) V = 2
Diff: 1 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using combined variation.
24) Write an equation that describes the variation.
F is inversely proportional to both λ and L. F = 
when λ = 7μm and L = 200 km.
A) F = 
B) F = 
C) F = 
D) F = 
Diff: 1 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using combined variation.
25) Hooke's Law in physics states that if a spring at rest (equilibrium position ) has a weight attached to it, then the distance the spring stretches is directly proportional to the force (weight).
F = kx
where F is the force in Newtons(N), x is the distance stretched in meters (m), and k is the spring constant (N/m).
A force of 352 N will stretch the spring 22 cm. How far will a force of 288 stretch the spring? Round to two decimal places.
A) 0.27 m
B) 26.89 m
C) 0.18 m
D) 18.00 m
Diff: 2 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using direct variation.
26) Hooke's Law in physics states that if a spring at rest (equilibrium position ) has a weight attached to it, then the distance the spring stretches is directly proportional to the force (weight).
F = kx
where F is the force in Newtons(N), x is the distance stretched in meters (m), and k is the spring constant (N/m).
A force of 429 N will stretch the spring 33 cm. How much force to the nearest Newtons is required to stretch the spring 72 cm?
A) 196.63 N
B) 936.00 N
C) 1,019,304.00 N
D) 9.36 N
Diff: 2 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using direct variation.
27) In physics, the inverse square law states that any physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity. In particular, the intensity of light radiating from a point source is inversely proportional to the square of the distance from the source. Below is a table of average distances from the Sun:
Planet | Distance to the Sun |
Mercury | 58,000 km |
Earth | 150,000 km |
Mars | 228,000 km |
The solar radiation on the Earth is approximately 1560 watts per square meter. How much solar radiation is there on Mercury? Round to the nearest hundred watts per square meter.
A) 605,172,413.79 watts per square meter
B) 4034.48 watts per square meter
C) 10,434.01 watts per square meter
D) 0.07 watts per square meter
Diff: 2 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using inverse variation.
28) A gas contained in a 3 mL container at a temperature of 340 K has a pressure of 1.5 atm. If the temperature decreases to 325 K, what is the resulting pressure?
A) 165,750.0 atm
B) 1.6 atm
C) 170.0 atm
D) 1.4 atm
Diff: 2 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using joint variation.
29) A gas contained in a 3 mL container at a temperature of 340 K has a pressure of 1 atm. If the container changes to a volume of 2 mL, what is the resulting pressure?
A) 113.3 atm
B) 0.7 atm
C) 1.5 atm
D) 6.0 atm
Diff: 2 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using joint variation.
30) Levi's makes jeans in a variety of price ranges for juniors. The Flare 519 jeans sell for about $19, whereas the 646 Vintage Flare jeans sell for $150. The demand for Levi's jeans is inversely proportional to the price. If 200,000 pairs of the Flare 519 jeans were bought, approximately how many of the 646 Vintage Flare were bought? Round to the nearest integer.
A) 1,578,947 pairs of the 646 Vintage Flare
B) 25,333 pairs of the 646 Vintage Flare
C) 1333 pairs of the 646 Vintage Flare
D) 10,526 pairs of the 646 Vintage Flare
Diff: 3 Var: 1
Chapter/Section: Ch 03, Sec 06
Learning Objective: Develop mathematical models using inverse variation.
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