تكلم مع الذكاء الاصطناعي
Deck 6: Exponential and Logarithmic Functions
ملء الشاشة (f)
سؤال
Identify the value of the function 
at 
. Round to 3 decimal places.
A) 6.028
B) 3.618
C) 2.618
D) 4.118
E) 3.118
at . Round to 3 decimal places.A) 6.028
B) 3.618
C) 2.618
D) 4.118
E) 3.118
سؤال
Rewrite the logarithmic equation 
in exponential form.
A)
B)
C)
D)
E)
in exponential form.A)
B)
C)
D)
E)
سؤال
Sketch the graph of the function 
سؤال
Use the One-to-One Property to solve the following equation for x. 
A)
B)
C)
D) 2
E)
A)
B)
C)
D) 2
E)
سؤال
Evaluate the function 
at 
. Round to 3 decimal places. (You may use your calculator.)
A) -3.391
B) 3.391
C) undefined
D) -2.928
E) 2.150
at . Round to 3 decimal places. (You may use your calculator.)A) -3.391
B) 3.391
C) undefined
D) -2.928
E) 2.150
سؤال
Identify the x-intercept of the function 
.
A)
B) The function has no x-intercept.
C)
D)
E)
.A)
B) The function has no x-intercept.
C)
D)
E)
سؤال
Evaluate the function 
at 
without using a calculator.
A)
B) -4
C) -2
D) 27
E) -3
at without using a calculator.A)
B) -4
C) -2
D) 27
E) -3
سؤال
Write the logarithmic equation 
in exponential form.
A)
B)
C)
D)
E)
in exponential form.A)
B)
C)
D)
E)
سؤال
Identify the graph of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Evaluate the function 
at 
. Round to 3 decimal places.
A) 1.690
B) 2.572
C) 5.287
D) 20.055
E) 4.680
at . Round to 3 decimal places.A) 1.690
B) 2.572
C) 5.287
D) 20.055
E) 4.680
سؤال
Let Q represent a mass of radioactive radium (226Ra) (in grams), whose half-life is 1599 years. The quantity of radium present after t years is 
Determine the quantity present after 300 years. Round to the nearest hundredth of a gram.
A) 0.00 g
B) 0.47 g
C) 5.00 g
D) 4.39 g
E) 0.88 g
Determine the quantity present after 300 years. Round to the nearest hundredth of a gram.A) 0.00 g
B) 0.47 g
C) 5.00 g
D) 4.39 g
E) 0.88 g
سؤال
What is the value of the function 
at 
? Round to 3 decimal places.
A) 1.398
B) 0.676
C) -7.747
D) 0.848
E) 1.795
at ? Round to 3 decimal places.A) 1.398
B) 0.676
C) -7.747
D) 0.848
E) 1.795
سؤال
Rewrite the exponential equation 
in logarithmic form.
A)
B)
C)
D)
E)
in logarithmic form.A)
B)
C)
D)
E)
سؤال
Evaluate the function 
at 
. Round to 3 decimal places. (You may use your calculator.)
A) undefined
B) 0.876
C) 0.147
D) 0.339
E) -0.347
at . Round to 3 decimal places. (You may use your calculator.)A) undefined
B) 0.876
C) 0.147
D) 0.339
E) -0.347
سؤال
Use a graphing utility to determine which graph below is the graph of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use the One-to-One Property to solve the following equation for x. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Solve the equation 
for x using the One-to-One Property.
A) -11
B) 0
C) The equation has no solution.
D) -9
E) 11
for x using the One-to-One Property.A) -11
B) 0
C) The equation has no solution.
D) -9
E) 11
سؤال
What is the value of the function 
at 
? Round to 3 decimal places.
A) 37.296
B) 26.492
C) 7.597
D) 42.051
E) 82.783
at ? Round to 3 decimal places.A) 37.296
B) 26.492
C) 7.597
D) 42.051
E) 82.783
سؤال
Write the exponential equation 
in logarithmic form.
A)
B)
C)
D)
E)
in logarithmic form.A)
B)
C)
D)
E)
سؤال
Evaluate the function 
at 
. Round to 3 decimal places.
A) 736.228
B) 803.695
C) 303.008
D) 54,270.000
E) 2.454
at . Round to 3 decimal places.A) 736.228
B) 803.695
C) 303.008
D) 54,270.000
E) 2.454
سؤال
Solve for x: 
. Round to 3 decimal places.
A) 7.587
B) 13.291
C) -3.794
D) -13.291
E) 10.518
. Round to 3 decimal places.A) 7.587
B) 13.291
C) -3.794
D) -13.291
E) 10.518
سؤال
Find the exact value of 
without using a calculator.
A) 1
B) 4
C) 9
D)
E)
without using a calculator.A) 1
B) 4
C) 9
D)
E)
سؤال
Find the exact value of 
without using a calculator.
A) 5
B) 2.5
C) 1.25
D) 2
E) 3
without using a calculator.A) 5
B) 2.5
C) 1.25
D) 2
E) 3
سؤال
سؤال
Simplify the expression 
.
A)
B)
C) 6
D) The expression cannot be simplified.
E)
.A)
B)
C) 6
D) The expression cannot be simplified.
E)
سؤال
Rewrite the logarithm 
in terms of the common logarithm (base 10).
A)
B)
C)
D)
E)
in terms of the common logarithm (base 10).A)
B)
C)
D)
E)
سؤال
Evaluate the logarithm 
using the change of base formula. Round to 3 decimal places.
A) 3.738
B) 1.921
C) 0.521
D) 7.273
E) 1.623
using the change of base formula. Round to 3 decimal places.A) 3.738
B) 1.921
C) 0.521
D) 7.273
E) 1.623
سؤال
سؤال
Determine whether or not 
is a solution to 
.
A) no
B) yes
is a solution to .A) no
B) yes
سؤال
Condense the expression 
to the logarithm of a single term.
A)
B)
C)
D)
E)
to the logarithm of a single term.A)
B)
C)
D)
E)
سؤال
The pH of an acidic solution is a measure of the concentration of the acid particles in the solution, with smaller values of the pH indicating higher acid concentration. In a laboratory experiment, the pH of a certain acid solution is changed by dissolving over-the-counter antacid tablets into the solution. In this experiment, the pH changes according to the equation 
, where x is the number of grams of antacid added to the solution. What is the pH of the solution after the addition of 0.1 grams of antacid tablet?
A) 5.14
B) 4.44
C) -0.18
D) 4.78
E) 4.96
, where x is the number of grams of antacid added to the solution. What is the pH of the solution after the addition of 0.1 grams of antacid tablet?A) 5.14
B) 4.44
C) -0.18
D) 4.78
E) 4.96
سؤال
Simplify the expression 
.
A) 4
B) The expression cannot be simplified.
C) -12
D) -108
E) 1
.A) 4
B) The expression cannot be simplified.
C) -12
D) -108
E) 1
سؤال
Evaluate the logarithm 
using the change of base formula. Round to 3 decimal places.
A) -1.745
B) -0.692
C) 0.630
D) 0.273
E) -0.573
using the change of base formula. Round to 3 decimal places.A) -1.745
B) -0.692
C) 0.630
D) 0.273
E) -0.573
سؤال
Condense the expression 
to the logarithm of a single term.
A)
B)
C)
D)
E)
to the logarithm of a single term.A)
B)
C)
D)
E)
سؤال
Solve 
for x.
A) -5
B) -1
C) -3
D) 1
E) no solution
for x.A) -5
B) -1
C) -3
D) 1
E) no solution
سؤال
Put the expressions in the appropriate order: 
.
A)
B)
C) The expressions are equivalent.
D)
E)
.A)
B)
C) The expressions are equivalent.
D)
E)
سؤال
Condense the expression 
to the logarithm of a single term.
A)
B)
C)
D)
E)
to the logarithm of a single term.A)
B)
C)
D)
E)
سؤال
Find the exact value of 
without using a calculator.
A)
B)
C)
D) -1
E)
without using a calculator.A)
B)
C)
D) -1
E)
سؤال
Rewrite the logarithm 
in terms of the natural logarithm.
A)
B)
C)
D)
E)
in terms of the natural logarithm.A)
B)
C)
D)
E)
سؤال
Solve for x: 
. Round to 3 decimal places.
A) 0.407
B) -1.362
C) 1.362
D) 2.407
E) no solution
. Round to 3 decimal places.A) 0.407
B) -1.362
C) 1.362
D) 2.407
E) no solution
سؤال
The chemical acidity of a solution is measured in units of pH: 
, where 
is the hydrogen ion concentration in the solution. What is 
if the 
?
A) 8.800
B)
C)
D)
E)
, where is the hydrogen ion concentration in the solution. What is if the ?A) 8.800
B)
C)
D)
E)
سؤال
The population P of a culture of bacteria is described by the equation 
, where t is the time, in hours, relative to the time at which the population was 1600.
(a) What was the population at
hours? Show your work.
(b) After how many hours will the population reach 8000? Round to the nearest tenth of an hour. Show your work.
, where t is the time, in hours, relative to the time at which the population was 1600.(a) What was the population at
hours? Show your work.(b) After how many hours will the population reach 8000? Round to the nearest tenth of an hour. Show your work.
سؤال
Carbon dating presumes that, as long as a plant or animal is alive, the proportion of its carbon that is 14C is constant. The amount of 14C in an object made from harvested plants, like paper, will decline exponentially according to the equation 
, where A represents the amount of 14C in the object, Ao represents the amount of 14C in living organisms, and t is the time in years since the plant was harvested. If an archeological artifact has 40% as much 14C as a living organism, how old would you predict it to be? Round to the nearest year.
A) 5715 years
B) 30,411 years
C) 87 years
D) 7554 years
E) 16,006 years
, where A represents the amount of 14C in the object, Ao represents the amount of 14C in living organisms, and t is the time in years since the plant was harvested. If an archeological artifact has 40% as much 14C as a living organism, how old would you predict it to be? Round to the nearest year.A) 5715 years
B) 30,411 years
C) 87 years
D) 7554 years
E) 16,006 years
سؤال
The chemical acidity of a solution is measured in units of pH: 
, where 
is the hydrogen ion concentration in the solution. If a sample of rain has a pH of 3.2, how many times higher is its 
than pure water's, which has a pH of 7?
A)
B)
C) 7
D)
E)
, where is the hydrogen ion concentration in the solution. If a sample of rain has a pH of 3.2, how many times higher is its than pure water's, which has a pH of 7?A)
B)
C) 7
D)
E)
سؤال
سؤال
The population P of a bacteria culture is modeled by 
, where t is the time in hours. If the population of the culture was 5800 after 40 hours, how long does it take for the population to double? Round to the nearest tenth of an hour.
A) 57.5 hours
B) 9.6 hours
C) 92.7 hours
D) 94.5 hours
E) 59.3 hours
, where t is the time in hours. If the population of the culture was 5800 after 40 hours, how long does it take for the population to double? Round to the nearest tenth of an hour.A) 57.5 hours
B) 9.6 hours
C) 92.7 hours
D) 94.5 hours
E) 59.3 hours
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العب
ملء الشاشة (f)
Deck 6: Exponential and Logarithmic Functions
1
Identify the value of the function at . Round to 3 decimal places.
A) 6.028
B) 3.618
C) 2.618
D) 4.118
E) 3.118
at . Round to 3 decimal places.A) 6.028
B) 3.618
C) 2.618
D) 4.118
E) 3.118
2.618
2
Rewrite the logarithmic equation in exponential form.
A)
B)
C)
D)
E)
in exponential form.A)
B)
C)
D)
E)
3
Sketch the graph of the function
4
Use the One-to-One Property to solve the following equation for x.
A)
B)
C)
D) 2
E)
A)
B)
C)
D) 2
E)
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5
Evaluate the function at . Round to 3 decimal places. (You may use your calculator.)
A) -3.391
B) 3.391
C) undefined
D) -2.928
E) 2.150
at . Round to 3 decimal places. (You may use your calculator.)A) -3.391
B) 3.391
C) undefined
D) -2.928
E) 2.150
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6
Identify the x-intercept of the function .
A)
B) The function has no x-intercept.
C)
D)
E)
.A)
B) The function has no x-intercept.
C)
D)
E)
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7
Evaluate the function at without using a calculator.
A)
B) -4
C) -2
D) 27
E) -3
at without using a calculator.A)
B) -4
C) -2
D) 27
E) -3
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8
Write the logarithmic equation in exponential form.
A)
B)
C)
D)
E)
in exponential form.A)
B)
C)
D)
E)
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9
Identify the graph of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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10
Evaluate the function at . Round to 3 decimal places.
A) 1.690
B) 2.572
C) 5.287
D) 20.055
E) 4.680
at . Round to 3 decimal places.A) 1.690
B) 2.572
C) 5.287
D) 20.055
E) 4.680
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11
Let Q represent a mass of radioactive radium (226Ra) (in grams), whose half-life is 1599 years. The quantity of radium present after t years is Determine the quantity present after 300 years. Round to the nearest hundredth of a gram.
A) 0.00 g
B) 0.47 g
C) 5.00 g
D) 4.39 g
E) 0.88 g
Determine the quantity present after 300 years. Round to the nearest hundredth of a gram.A) 0.00 g
B) 0.47 g
C) 5.00 g
D) 4.39 g
E) 0.88 g
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12
What is the value of the function at ? Round to 3 decimal places.
A) 1.398
B) 0.676
C) -7.747
D) 0.848
E) 1.795
at ? Round to 3 decimal places.A) 1.398
B) 0.676
C) -7.747
D) 0.848
E) 1.795
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13
Rewrite the exponential equation in logarithmic form.
A)
B)
C)
D)
E)
in logarithmic form.A)
B)
C)
D)
E)
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14
Evaluate the function at . Round to 3 decimal places. (You may use your calculator.)
A) undefined
B) 0.876
C) 0.147
D) 0.339
E) -0.347
at . Round to 3 decimal places. (You may use your calculator.)A) undefined
B) 0.876
C) 0.147
D) 0.339
E) -0.347
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15
Use a graphing utility to determine which graph below is the graph of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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16
Use the One-to-One Property to solve the following equation for x.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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17
Solve the equation for x using the One-to-One Property.
A) -11
B) 0
C) The equation has no solution.
D) -9
E) 11
for x using the One-to-One Property.A) -11
B) 0
C) The equation has no solution.
D) -9
E) 11
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18
What is the value of the function at ? Round to 3 decimal places.
A) 37.296
B) 26.492
C) 7.597
D) 42.051
E) 82.783
at ? Round to 3 decimal places.A) 37.296
B) 26.492
C) 7.597
D) 42.051
E) 82.783
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19
Write the exponential equation in logarithmic form.
A)
B)
C)
D)
E)
in logarithmic form.A)
B)
C)
D)
E)
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20
Evaluate the function at . Round to 3 decimal places.
A) 736.228
B) 803.695
C) 303.008
D) 54,270.000
E) 2.454
at . Round to 3 decimal places.A) 736.228
B) 803.695
C) 303.008
D) 54,270.000
E) 2.454
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21
Solve for x: . Round to 3 decimal places.
A) 7.587
B) 13.291
C) -3.794
D) -13.291
E) 10.518
. Round to 3 decimal places.A) 7.587
B) 13.291
C) -3.794
D) -13.291
E) 10.518
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22
Find the exact value of without using a calculator.
A) 1
B) 4
C) 9
D)
E)
without using a calculator.A) 1
B) 4
C) 9
D)
E)
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23
Find the exact value of without using a calculator.
A) 5
B) 2.5
C) 1.25
D) 2
E) 3
without using a calculator.A) 5
B) 2.5
C) 1.25
D) 2
E) 3
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24
An initial investment of $3000 doubles in value in 8.3 years. Assuming continuous compounding, what was the interest rate? Round to the nearest tenth of a percent.
A) 8.4%
B) 3.6%
C) 4.2%
D) 8.3%
E) 100%
A) 8.4%
B) 3.6%
C) 4.2%
D) 8.3%
E) 100%
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25
Simplify the expression .
A)
B)
C) 6
D) The expression cannot be simplified.
E)
.A)
B)
C) 6
D) The expression cannot be simplified.
E)
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26
Rewrite the logarithm in terms of the common logarithm (base 10).
A)
B)
C)
D)
E)
in terms of the common logarithm (base 10).A)
B)
C)
D)
E)
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27
Evaluate the logarithm using the change of base formula. Round to 3 decimal places.
A) 3.738
B) 1.921
C) 0.521
D) 7.273
E) 1.623
using the change of base formula. Round to 3 decimal places.A) 3.738
B) 1.921
C) 0.521
D) 7.273
E) 1.623
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28
Which investment option will pay the most interest?
A) 11.2% compounded quarterly
B) 11.4% compounded semiannually
C) 11.0% compounded continuously
D) These investments all pay the same amount of interest.
E) 11.6% compounded annually
A) 11.2% compounded quarterly
B) 11.4% compounded semiannually
C) 11.0% compounded continuously
D) These investments all pay the same amount of interest.
E) 11.6% compounded annually
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29
Determine whether or not is a solution to .
A) no
B) yes
is a solution to .A) no
B) yes
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30
Condense the expression to the logarithm of a single term.
A)
B)
C)
D)
E)
to the logarithm of a single term.A)
B)
C)
D)
E)
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31
The pH of an acidic solution is a measure of the concentration of the acid particles in the solution, with smaller values of the pH indicating higher acid concentration. In a laboratory experiment, the pH of a certain acid solution is changed by dissolving over-the-counter antacid tablets into the solution. In this experiment, the pH changes according to the equation , where x is the number of grams of antacid added to the solution. What is the pH of the solution after the addition of 0.1 grams of antacid tablet?
A) 5.14
B) 4.44
C) -0.18
D) 4.78
E) 4.96
, where x is the number of grams of antacid added to the solution. What is the pH of the solution after the addition of 0.1 grams of antacid tablet?A) 5.14
B) 4.44
C) -0.18
D) 4.78
E) 4.96
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32
Simplify the expression .
A) 4
B) The expression cannot be simplified.
C) -12
D) -108
E) 1
.A) 4
B) The expression cannot be simplified.
C) -12
D) -108
E) 1
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33
Evaluate the logarithm using the change of base formula. Round to 3 decimal places.
A) -1.745
B) -0.692
C) 0.630
D) 0.273
E) -0.573
using the change of base formula. Round to 3 decimal places.A) -1.745
B) -0.692
C) 0.630
D) 0.273
E) -0.573
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34
Condense the expression to the logarithm of a single term.
A)
B)
C)
D)
E)
to the logarithm of a single term.A)
B)
C)
D)
E)
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35
Solve for x.
A) -5
B) -1
C) -3
D) 1
E) no solution
for x.A) -5
B) -1
C) -3
D) 1
E) no solution
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36
Put the expressions in the appropriate order: .
A)
B)
C) The expressions are equivalent.
D)
E)
.A)
B)
C) The expressions are equivalent.
D)
E)
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37
Condense the expression to the logarithm of a single term.
A)
B)
C)
D)
E)
to the logarithm of a single term.A)
B)
C)
D)
E)
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38
Find the exact value of without using a calculator.
A)
B)
C)
D) -1
E)
without using a calculator.A)
B)
C)
D) -1
E)
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39
Rewrite the logarithm in terms of the natural logarithm.
A)
B)
C)
D)
E)
in terms of the natural logarithm.A)
B)
C)
D)
E)
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40
Solve for x: . Round to 3 decimal places.
A) 0.407
B) -1.362
C) 1.362
D) 2.407
E) no solution
. Round to 3 decimal places.A) 0.407
B) -1.362
C) 1.362
D) 2.407
E) no solution
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41
The chemical acidity of a solution is measured in units of pH: , where is the hydrogen ion concentration in the solution. What is if the ?
A) 8.800
B)
C)
D)
E)
, where is the hydrogen ion concentration in the solution. What is if the ?A) 8.800
B)
C)
D)
E)
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42
The population P of a culture of bacteria is described by the equation , where t is the time, in hours, relative to the time at which the population was 1600.
(a) What was the population at hours? Show your work.
(b) After how many hours will the population reach 8000? Round to the nearest tenth of an hour. Show your work.
, where t is the time, in hours, relative to the time at which the population was 1600.(a) What was the population at
hours? Show your work.(b) After how many hours will the population reach 8000? Round to the nearest tenth of an hour. Show your work.
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43
Carbon dating presumes that, as long as a plant or animal is alive, the proportion of its carbon that is 14C is constant. The amount of 14C in an object made from harvested plants, like paper, will decline exponentially according to the equation , where A represents the amount of 14C in the object, Ao represents the amount of 14C in living organisms, and t is the time in years since the plant was harvested. If an archeological artifact has 40% as much 14C as a living organism, how old would you predict it to be? Round to the nearest year.
A) 5715 years
B) 30,411 years
C) 87 years
D) 7554 years
E) 16,006 years
, where A represents the amount of 14C in the object, Ao represents the amount of 14C in living organisms, and t is the time in years since the plant was harvested. If an archeological artifact has 40% as much 14C as a living organism, how old would you predict it to be? Round to the nearest year.A) 5715 years
B) 30,411 years
C) 87 years
D) 7554 years
E) 16,006 years
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44
The chemical acidity of a solution is measured in units of pH: , where is the hydrogen ion concentration in the solution. If a sample of rain has a pH of 3.2, how many times higher is its than pure water's, which has a pH of 7?
A)
B)
C) 7
D)
E)
, where is the hydrogen ion concentration in the solution. If a sample of rain has a pH of 3.2, how many times higher is its than pure water's, which has a pH of 7?A)
B)
C) 7
D)
E)
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45
An initial investment of $9000 grows at an annual interest rate of 5% compounded continuously. How long will it take to double the investment?
A) 1 year
B) 14.40 years
C) 13.86 years
D) 14.86 years
E) 13.40 years
A) 1 year
B) 14.40 years
C) 13.86 years
D) 14.86 years
E) 13.40 years
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46
The population P of a bacteria culture is modeled by , where t is the time in hours. If the population of the culture was 5800 after 40 hours, how long does it take for the population to double? Round to the nearest tenth of an hour.
A) 57.5 hours
B) 9.6 hours
C) 92.7 hours
D) 94.5 hours
E) 59.3 hours
, where t is the time in hours. If the population of the culture was 5800 after 40 hours, how long does it take for the population to double? Round to the nearest tenth of an hour.A) 57.5 hours
B) 9.6 hours
C) 92.7 hours
D) 94.5 hours
E) 59.3 hours
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