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Modeling with Exponential and Logarithmic Equations Answers

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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%
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. A basic solution has a pH of 11.2. An acidic solution has a pH of 2.4. What is the approximate difference in the concentration of hydrogen ions between the two solutions?

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The amount of a sample remaining after t days is given by the equation , where A is the initial amount of the sample and h is the half-life, in days, of the substance. A scientist has a 10-mg sample of a radioactive isotope. The isotope has a half-life of 8 days. After 16 days, how much of the radioactive isotope remains?

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A
2.0 mg
B
2.5 mg
C
5.7 mg
D
7.1 mg
4

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 D
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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
6

The amount of a sample remaining after t days is given by the equation , where A is the initial amount of the sample and h is the half-life, in days, of the substance. A sample contains 60% of its original amount of Fermium-257. The half-life of Fermium-257 is about 100 days. About how old is the sample?

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A
52 days
B
60 days
C
74 days
D
136 days
7

A pizza is taken out of an oven and placed on a counter. The temperature, T, in degrees Fahrenheit, of the pizza after m minutes is modeled by the function . Which graph represents the model?

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Option D
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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
9

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
10

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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11

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
12

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 ?

Question illustration
A
1.0
B
2.9
C
8.7
D
9.3
13

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?

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Option A
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Option B
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Option C
D
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Option D
14

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

Question illustration
A
0.40
B
1.02
C
1.05
D
2.51
15

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

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Option A
B
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C
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Option C
D
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Option D
16

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

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A
5.9 years
B
6.1 years
C
23.4 years
D
24.5 years
17

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

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A
$6,360.00
B
$6,370.78
C
$7,180.89
D
$10,892.13
18

The pH of a particular solution is given by , where x represents the concentration of the hydrogen ions in the solution, in moles per liter. Which graph models the pH of this solution?

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B
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Option C
D
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Option D
19

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

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Option A
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Option D
20

Jacques deposited $1,900 into an account that earns 4% interest compounded semiannually. After t years, Jacques has $3,875.79 in the account. Assuming he made no additional deposits or withdrawals, how long was the money in 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
2 years
B
9 years
C
18 years
D
36 years

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