AnswersFL-1200330-Algebra 2 CRModeling with Exponential and Logarithmic Equations

Modeling with Exponential and Logarithmic Equations — Unit test Answers

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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?

1
1.7 years
2
2.0 years
3
3.1 years
5
5.0 years
2
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Which function has a horizontal asymptote of y = 3?

A
f(x) = 3(2x)
B
f(x) = 2(4)x–3
C
f(x) = 2(3x)
D
f(x) = 2(4x) + 3
3

What is written as a single logarithm?

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Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
4

Which equation has x = 4 as the solution?

Question illustration
A
log Subscript 4 Baseline (3 x + 4) = 2
Option A
B
log Subscript 3 Baseline (2 x minus 5) = 2
Option B
C
log Subscript x Baseline 64 = 4
Option C
D
log Subscript x Baseline 16 = 4
Option D
5

Which is the graph of ?

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A
On a coordinate plane, a curve starts at (2, 0) and curves up and goes through (3, 3) and (9, 5).
Option A
B
Option
Option B
C
Option
Option C
D
On a coordinate plane, a curve starts at (2, 6) and curves down and goes through (3, 3) and (10, 2).
Option D
6

An equation for the depreciation of a car is given by y = A(1 – r)t, where y = current value of the car, A = original cost, r = rate of depreciation, and t = time, in years. The current value of a car is $12,282.50. The car originally cost $20,000 and depreciates at a rate of 15% per year. How old is the car?

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y
years
Option y
y
years
Option y
3
3 years
4
4 years
7

What is the domain of the function

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A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
8

Which statement best compares the graphs of and ?

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T
The two graphs are exactly the same.
T
The open and closed circles are reversed.
T
The graph of is shifted up compared to the graph of , and the open and closed circles are reversed.
Option T
T
The graph of is shifted up compared to the graph of , and the open and closed circles are the same.
Option T
9

Identify the equation that translates five units down.

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Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
10

Which expression is equivalent to ?

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Option
Option A
B
Option
Option B
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Option
Option C
D
Option
Option D
11

The magnitude, M, of an earthquake is defined to be , where I is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and S is the intensity of a “standard” earthquake, which is barely detectable. What is the magnitude of an earthquake that is 1,000 times more intense than a standard earthquake? Use a calculator. Round your answer to the nearest tenth.

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A
2
B
3
C
4.5
D
6.9
12

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
13

What is the range of the function graphed below?

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Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
14

One brand of vinegar has a pH of 4.5. Another brand has a pH of 5.0. The equation for the pH of a substance is pH = –log[H+], where H+ is the concentration of hydrogen ions. What is the approximate difference in the concentration of hydrogen ions between the two brands of vinegar?

A
mc017-1.jpg
Option A
B
mc017-2.jpg
Option B
C
mc017-3.jpg
Option C
D
mc017-4.jpg
Option D
15

A farmer sells almonds according to the chart below. The more pounds of almonds that are sold, the lower the cost per pound is for the entire order of almonds.Almond PricesNumber of PoundsCost (per Pound)up to 10$20 more than 10, and up to 20$15 more than 20, and up to 30$10 more than 30$5 The farmer graphs a step function to model the situation, where y represents the cost per pound for an order of x pounds of almonds. Which of the following describes the farmer’s graph for the step that includes 20.75 pounds, and what is the total cost of 20.75 pounds of almonds?

A
a horizontal segment with an open circle at (20, 10) and a closed circle at (30, 10); $207.50
B
a horizontal segment with a closed circle at (20, 10) and an open circle at (30, 10); $207.50
C
a horizontal segment with an open circle at (21, 10) and a closed circle at (30, 10); $311.25
D
a horizontal segment with a closed circle at (21, 10) and an open circle at (30, 10); $311.25
16

What are the domain and range of ?

Question illustration
A
domain: x > 1; range: y > 2
B
domain: x > 1; range: all real numbers
C
domain: all real numbers; range: y > 1
D
domain: all real numbers; range: all real numbers
17

What is the range of ?

Question illustration
A
all real numbers not equal to 0
B
all real numbers less than 6
C
all real number greater than 6
D
all real numbers
18

Which of the following shows the graph of

Question illustration
A
On a coordinate plane, a curve approaches the y-axis in quadrant 3. It increases into quadrant 2 and crosses the x-axis at (negative 0.5, 0).
Option A
B
On a coordinate plane, a curve approaches the y-axis in quadrant 3. It increases into quadrant 2 and crosses the x-axis at (negative 4, 0).
Option B
C
On a coordinate plane, a curve approaches the y-axis in quadrant 4. It increases into quadrant 1 and crosses the x-axis at (0.5, 0).
Option C
D
On a coordinate plane, a curve approaches the y-axis in quadrant 4. It increases into quadrant 1 and crosses the x-axis at (4, 0).
Option D
19

A student showed the steps below while solving the equation by graphing.Step 1:Write a system of equations: Step 2: Use the change of base formula to rewrite the equations:Step 3:Graph the two equations:Step 4:Identify the x-value at the point of intersection:In which step did the student make the first error?

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A
step 1
B
step 2
C
step 3
D
step 4
20

Which of the following accurately lists all discontinuities of the function below?

Question illustration
A
point discontinuity at x = –2
B
point discontinuity at x = 4; jump discontinuity at x = –2
C
point discontinuities at x = –4 and x = 4; jump discontinuity at x = –2
D
jump discontinuities at x = –4, x = –2, and x = 4

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