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

Modeling with Exponential and Logarithmic Equations Answers

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Which point corresponds to the real zero of the graph of ?

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Option A
B
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Option B
C
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Option C
D
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Option D
2
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The equation for the pH of a substance is pH = –log[H+], where H+ is the concentration of hydrogen ions. What is the approximate pH of a solution whose hydrogen ion concentration is ?

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A
1.0
B
2.9
C
8.7
D
9.3
3

The general equation for depreciation is given by y = A(1 – r)t, where y = current value, A = original cost, r = rate of depreciation, and t = time, in years. A car was purchased 6 years ago for $25,000. If the annual depreciation rate is 11%, which equation can be used to determine the approximate current value of the car?

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

Which equation would have real zero(s) corresponding to the x-intercept(s) of the graph below?

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Option A
B
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Option B
C
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Option C
D
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Option D
5

Over time, the number of organisms in a population increases exponentially. The table below shows the approximate number of organisms after y years. y yearsnumber of organisms, n155260367475The environment in which the organism lives can support at most 600 organisms. Assuming the trend continues, after how many years will the environment no longer be able to support the population?

A
12
B
24
C
61
D
82
6

The estimated number of organisms in a population after t days is shown in the table below.t daysestimated number of organisms, n286041,25061,80082,600103,720Which equation best models the situation?

A
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Option A
B
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Option B
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Option C
D
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Option D
7

Isabel deposits $6,000 into an account that earns 1.5% interest compounded monthly. Assuming no more deposits and no withdrawals are made, how much money is in the account after 4 years?Compound interest formula:t = years since initial depositn = number of times compounded per yearr = annual interest rate (as a decimal)P = initial (principal) investmentV(t) = value of investment after t years

Question illustration
A
$6,360.00
B
$6,370.78
C
$7,180.89
D
$10,892.13
8

A type of plant is introduced into an ecosystem and quickly begins to take over. A scientist counts the number of plants after m months and develops the equation to model the situation. Most recently, the scientist counted 138 plants. Assuming there are no limiting factors to the growth of the plants, about how many months have passed since the plants were first introduced?

Question illustration
A
6.1
B
6.6
C
7.2
D
23.1
9

The loudest sound measured one night during a hockey game was 112 dB. The loudest sound measured during a hockey game the next night was 118 dB. What fraction of sound intensity of the second game was the sound intensity of the first game?L = loudness, in decibelsI = sound intensity, in watts/m2I0 = 10–12 watts/m2

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A
0.25
B
0.78
C
0.95
D
0.99
10

The equation for the pH of a substance is pH = –log[H+], where H+ is the concentration of hydrogen ions. Which equation models the concentration of hydrogen ions (H+) of a solution whose pH is 7.2?

A
[H+] = log7.2
B
[H+] = -log7.2
C
[H+] =
Option C
D
[H+] =
Option D
11

Over time, the number of organisms in a population increases exponentially. The table below shows the approximate number of organisms after y years. y yearsnumber of organisms, n155260367475The environment in which the organism lives can support at most 600 organisms. Assuming the trend continues, after how many years will the environment no longer be able to support the population?

A
12
B
24
C
61
D
82
12

Isabel deposits $6,000 into an account that earns 1.5% interest compounded monthly. Assuming no more deposits and no withdrawals are made, how much money is in the account after 4 years?Compound interest formula:t = years since initial depositn = number of times compounded per yearr = annual interest rate (as a decimal)P = initial (principal) investmentV(t) = value of investment after t years

Question illustration
A
$6,360.00
B
$6,370.78
C
$7,180.89
D
$10,892.13
13

A sum of money is invested at 12% compounded quarterly. About how long will it take for the amount of money to double?Compound interest formula:t = years since initial depositn = number of times compounded per yearr = annual interest rate (as a decimal)P = initial (principal) investmentV(t) = value of investment after t years

Question illustration
A
5.9 years
B
6.1 years
C
23.4 years
D
24.5 years
14

When Akbar’s son was four years old, Akbar put $250 into an account that guaranteed a 10% annual return. The equation represents the amount of money in the account when the child will be x years old.Which graph models the scenario?

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Option A
B
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Option B
C
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Option C
D
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Option D
15

How would you describe the relationship between the real zeros and x-intercepts of the function ?

Question illustration
A
When you set the function equal to zero, the solution is x = 6; therefore, the graph has an x-intercept at x = 6.
B
When you substitute x = 0 into the function there is no solution; therefore, the graph will not have any x-intercepts.
C
Since there is an asymptote at x = 2, the graph will not have an x-intercept; therefore, the function will have no real zeros.
D
When you set the function equal to zero, the solution is x = 3; therefore, the graph has an x-intercept at x = 3.
16

A type of plant is introduced into an ecosystem and quickly begins to take over. A scientist counts the number of plants after m months and develops the equation to model the situation. Most recently, the scientist counted 138 plants. Assuming there are no limiting factors to the growth of the plants, about how many months have passed since the plants were first introduced?

Question illustration
A
6.1
B
6.6
C
7.2
D
23.1
17

On April 11, 2012, two earthquakes were measured off the northwest coast of Sumatra. The first had a magnitude of 8.6. The second had a magnitude of 8.2. By what approximate factor was the intensity of the first earthquake greater than the intensity of the second earthquake?M = the magnitude of an earthquakeI = the intensity of an earthquakeI0 = the smallest seismic activity that can be measured, which is 1

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A
0.40
B
1.02
C
1.05
D
2.51
18

Which point corresponds to the real zero of the graph of ?

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Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
19

Claire deposited $2,500 into an account that accrues interest monthly. She made no additional deposits or withdrawals. After 2 years, Claire had $2,762.35 in the account. What is the annual interest rate of the account?Compound interest formula:t = years since initial depositn = number of times compounded per yearr = annual interest rate (as a decimal)P = initial (principal) investmentV(t) = value of investment after t years

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A
5%
B
11%
C
26%
D
31%
20

Food poisoning occurs when bacteria like Salmonella and Listeria grow on food. These microorganisms grow at an exponential rate. When an initial population of 100 bacteria are left at , they will grow at a rate of . Which graph could be used to calculate the number of bacteria after a certain number of hours?

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Option A
B
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Option B
C
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Option C
D
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Option D

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