AnswersPBCSD_Grade_Forgiveness_1200330_Algebra 2_S2_2024Modeling with Exponential and Logarithmic Equations

Modeling with Exponential and Logarithmic Equations — Unit test Answers

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1
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Which graph shows the solution to the equation below?

Question illustration
A
On a coordinate plane, a curve starts in quadrant 3 and curves up into quadrant 1 and approaches y = 3. It crosses the x-axis at (1, 0). A horizontal straight line is at y = 1.
Option A
B
On a coordinate plane, a curves starts in quadrant 4 and curves up into quadrant 1 and approaches y = 3. It crosses the x-axis at (1, 0). A horizontal straight line is at y = negative 1.
Option B
C
On a coordinate plane, a curve starts in quadrant 3 and curves up into quadrant 1 and approaches y = 1. It crosses the x-axis at (negative 1, 0). A horizontal straight line is at y = 1.
Option C
D
On a coordinate plane, a curves starts in quadrant 3 and curves up into quadrant 1 and approaches y = 2. It crosses the x-axis at (negative 1, 0). A horizontal straight line is at y = negative 1.
Option D
2
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What is the range of the function f(x) = –2(6x) + 3?

A
(negative infinity, negative 2 Right-bracket
Option A
B
(negative infinity, 3)
Option B
C
Left-bracket negative 2, infinity)
Option C
D
Left-bracket 3, infinity)
Option D
3

A scientist writes the equation to model the growth of a certain bacteria in a petri dish, where N represents the number of bacteria after h hours. After approximately how many hours will 450 bacteria be present? Round your answer to the nearest whole number.

Question illustration
A
1 hour
B
6 hours
C
13 hours
D
15 hours
4

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
5

Which is the graph of ?

Question illustration
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
mc026-3.jpg
Option B
C
mc026-4.jpg
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

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
7

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
8

What are the solutions to

Question illustration
A
x = negative 2 and x = negative 4
Option A
B
x = negative 1 and x = 8
Option B
C
x = 1 and x = negative 8
Option C
D
x = 2 and x = 4
Option D
9

For what values of x does ?

Question illustration
A
x = –3, x = 1
B
x = –1, x = 3
C
x = negative three-halves, x = 2
Option C
D
x = negative 2, x = three-halves
Option D
10

An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded continuously. The equation represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use a calculator and round your answer to the nearest whole number.

Question illustration
A
5 years
B
7 years
C
19 years
D
22 years
11

If , what is the value of x?

Question illustration
A
–3
B
–2
C
2
D
3
12

What is the solution of Round your answer to the nearest hundredth.

Question illustration
A
mc017-2.jpg
Option A
B
mc017-3.jpg
Option B
C
mc017-4.jpg
Option C
D
mc017-5.jpg
Option D
13

What is the solution to

Question illustration
A
mc004-2.jpg
Option A
B
mc004-3.jpg
Option B
C
mc004-4.jpg
Option C
D
mc004-5.jpg
Option D
14

Which of the following shows the graph of y = –(2)x – 1?

A
On a coordinate plane, a curve is level at y = 0 in quadrant 2 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, negative 0.5).
Option A
B
On a coordinate plane, a curve is level at y = negative 1 in quadrant 3 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, negative 2).
Option B
C
On a coordinate plane, a curve is level at y = 1 in quadrant 3 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, 0).
Option C
D
On a coordinate plane, a curve is level at y = 0 in quadrant 2 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, negative 2).
Option D
15

If , what is the value of x?

Question illustration
A
Five-eighths
Option A
B
Eight-fifths
Option B
C
2
D
8

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