AnswersCUSD Advanced Math A 5.0Exponential and Logarithmic Inequalities

Exponential and Logarithmic Inequalities — Unit test Answers

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Regular exercise can help a person lower their resting heart rate. Suppose an individual’s resting heart rate, in beats per minute, is modeled by the function f(x) = –0.1x 3 + 0.6x 2 + 85 after x weeks of regular exercise.How many weeks of exercise are necessary to lower the individual’s resting heart rate below 70 beats per minute?

A
7 weeks
B
8 weeks
C
9 weeks
D
10 weeks
2
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What is the solution of ?

Question illustration
A
–1 < x < 1 or
Option A
B
–1 < x < 1 or
Option B
C
x < –1 or
Option C
D
x < –1 or
Option D
3

A cliff diver leaps from a 100-foot cliff into the Pacific. The diver’s height above the water is modeled by the functionP(x) = –16x 2 + 10x + 100, where x is time in seconds.During which interval is the diver at least halfway down?

A
2.0 < x < 2.1 seconds
B
2.1 < x < 2.8 seconds
C
3.0 < x < 3.4 seconds
D
3.4 < x < 3.5 seconds
4

What are the roots of the polynomial equation ? Use a graphing calculator and a system of equations.

Question illustration
A
–2, –1, 0, 2
B
–2, 0, 1, 2
C
–1, 0
D
0, 1
5

A rectangular prism with a volume of 400 cubic centimeters has the dimensions x + 1 centimeters, 2x centimeters, and x + 6 centimeters. The equation can be used to find x. What is the length of the longest side? Use a graphing calculator and a system of equations to find the answer.

Question illustration
A
4 centimeters
B
5 centimeters
C
8 centimeters
D
10 centimeters
6

What is the solution to x 4 + 4x 3 ≤ 12x 2?

A
(–6, 2)
B
[–6, 2]
C
(–ꝏ, –6) U (2, ꝏ)
D
(–ꝏ, –6] U [2, ꝏ)
7

What is the solution to 4x 3 – 3x 2 – 7x < 0?

A
(–ꝏ, –1) U (0, 1.75)
B
(–ꝏ, –1] U [0, 1.75]
C
(–1, 0) U (1.75, ꝏ)
D
[–1, 0] U [1.75, ꝏ)
8

You can use a system of equations to graph and solve the polynomial equation . Which statement is true?

Question illustration
A
The system has one solution, and the equation has three zeroes.
B
The y-coordinates of the solutions to the system and the zeroes of the equation are not equal.
C
The x-coordinates of the solutions to the system and the zeroes of the equation are not equal.
D
The equation has one zero, and the system has three solutions.
9

Two different radioactive isotopes decay to 10% of their respective original amounts. Isotope A does this in 33 days, while isotope B does this in 43 days. What is the approximate difference in the half-lives of the isotopes?

A
3 days
B
10 days
C
13 days
D
33 days
10

Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of 10%. The second car depreciates at an annual rate of 15%. What is the approximate difference in the ages of the two cars?

A
1.7 years
B
2.0 years
C
3.1 years
D
5.0 years
11

What are the roots of the polynomial equation ? Use a graphing calculator and a system of equations.

Question illustration
A
–24, –3, 12
B
–12, 3, 24
C
–4, –2, 3
D
–3, 2, 4
12

What is written as a single logarithm?

Question illustration
A
4 log Subscript one-half Baseline 2 Superscript 4 Baseline u squared minus v cubed
Option A
B
log Subscript one-half Baseline w Superscript 4 Baseline (StartFraction u squared Over v cubed EndFraction)
Option B
C
log Subscript one-half Baseline (StartFraction w Superscript 4 Baseline Over u squared v cubed EndFraction)
Option C
D
log Subscript one-half Baseline (w (StartFraction u squared Over v cubed EndFraction)) Superscript 4
Option D
13

What is the partial fraction decomposition of ?

A
StartFraction negative 2 Over 2 x minus 5 EndFraction + StartFraction 7 Over x minus 4 EndFraction
B
StartFraction 7 Over 2 x minus 5 EndFraction + StartFraction negative 2 Over x minus 4 EndFraction
C
StartFraction 2 Over 2 x minus 5 EndFraction + StartFraction 7 Over x minus 4 EndFraction
D
StartFraction 7 Over 2 x minus 5 EndFraction + StartFraction 2 Over x minus 4 EndFraction
14

Review the equation used in writing a partial fraction decomposition.

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
15

What is the correct form of the partial fraction decomposition for ?

A
StartFraction A Over 4 x EndFraction + StartFraction B Over x + 7 EndFraction
B
StartFraction A Over 4 x squared EndFraction + StartFraction B Over 28 x EndFraction
C
StartFraction A x + B Over 4 x EndFraction + StartFraction C Over x + 7 EndFraction
D
StartFraction A x + B Over 4 x squared EndFraction + StartFraction C Over 28 x EndFraction

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