Question 1

Condense the expression to the logarithm of a single quantity. ​  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 2

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 0.05 grams of antacid tablet?

Accepted Answer

A) 5.99 
B) 4.02 
C) -0.85 
D) 4.29 
E) 5.14

Question 3

The populations P (in thousands) of Pittsburgh, Pennsylvania from 2000 through 2007 can be modeled by  where t represents the year, with  corresponding to 2000.Use the model to find the numbers of cell sites in the year 2009.
​

Accepted Answer

A) 2,326,853.00 
B) 2,327,853.00 
C) 2,329,853.00 
D) 2,328,853.00 
E) 2,330,853.00

Question 4

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 3.3, how many times higher is its  than pure water's, which has a pH of 7?

Accepted Answer

A)   
B)   
C)   
D)   
E) 7

Question 5

Rewrite the logarithm as a ratio of natural logarithms. ​  ​

Accepted Answer

A)   
B)   
C)   
D)   
E) None of these

Question 6

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.

Accepted Answer

A) 54.8 hours 
B) 8.9 hours 
C) 79.9 hours 
D) 81.7 hours 
E) 56.6 hours

Question 7

Use the One-to-One Property to solve the following equation for x.  ​

Accepted Answer

A)   
B)   
C)   
D) 2 
E)

Question 8

Solve for x. ​  ​

Accepted Answer

A) 4 
B)   
C) 7 
D) 3 
E)

Question 9

given that f(x) = ln x.
​
f(x - 7) = f(x) - f(7), x > 0
​

Accepted Answer

A) True 
 B)False

Question 10

Evaluate the function at the indicated value of  . ​  ​

Accepted Answer

A) 7 
B) 0 
C)   
D) -7 
E)

Question 11

$5500 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to double.(Approximate the result to two decimal places.) ​  ​

Accepted Answer

A) 13.84 yr 
B) 10.84 yr 
C) 12.84 yr 
D) 11.84 yr 
E) 14.84 yr

Question 12

Select the graph of the exponential function. ​
​  ​

Accepted Answer

A) ​  ​ 
B) ​  
C) ​  
D) ​  
E) ​

Question 13

Solve the exponential equation algebraically.Approximate the result to three decimal places. ​  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 14

Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years.Of an initial sample of 33 grams, how much will remain after 69 years? ​

Accepted Answer

A) 0 grams 
B) 29.1351 grams 
C) 10.9074 grams 
D) 8.2500 grams 
E) 0.6973 grams

Question 15

Select the graph of the function. ​  ​

Accepted Answer

A) ​  
B) ​  
C) ​  
D) ​  
E) ​

Question 16

Write the exponential equation in logarithmic form. ​  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 17

Solve the equation algebraically.Round the result to three decimal places. ​  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 18

Solve the exponential equation algebraically.Approximate the result to three decimal places. ​  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 19

Use the properties of logarithms to simplify the expression. ​  ​

Accepted Answer

A) 17 
B) 0 
C)   
D) -17 
E)

Question 20

Which investment option will pay the most interest?

Accepted Answer

A) 10.2% compounded quarterly 
B) 10.4% compounded semiannually 
C) 10.0% compounded continuously 
D) These investments all pay the same amount of interest. 
E) 10.6% compounded annually

Exam 5: Exponential-And-Logarithmic-Functions

Condense the expression to the logarithm of a single quantity.

The populations P (in thousands) of Pittsburgh, Pennsylvania from 2000 through 2007 can be modeled by where t represents the year, with corresponding to 2000.Use the model to find the numbers of cell sites in the year 2009.

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 3.3, how many times higher is its than pure water's, which has a pH of 7?

Rewrite the logarithm as a ratio of natural logarithms.

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.

Use the One-to-One Property to solve the following equation for x.

Solve for x.

given that f(x) = ln x. f(x - 7) = f(x) - f(7), x > 0

Evaluate the function at the indicated value of .

$5500 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to double.(Approximate the result to two decimal places.)

Select the graph of the exponential function.

Solve the exponential equation algebraically.Approximate the result to three decimal places.

Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years.Of an initial sample of 33 grams, how much will remain after 69 years?

Select the graph of the function.

Write the exponential equation in logarithmic form.

Solve the equation algebraically.Round the result to three decimal places.

Solve the exponential equation algebraically.Approximate the result to three decimal places.

Use the properties of logarithms to simplify the expression.

Which investment option will pay the most interest?

Exam 5: Exponential-And-Logarithmic-Functions

Condense the expression to the logarithm of a single quantity. ​ ​

The populations P (in thousands) of Pittsburgh, Pennsylvania from 2000 through 2007 can be modeled by where t represents the year, with corresponding to 2000.Use the model to find the numbers of cell sites in the year 2009. ​

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 3.3, how many times higher is its than pure water's, which has a pH of 7?

Rewrite the logarithm as a ratio of natural logarithms. ​ ​

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.

Use the One-to-One Property to solve the following equation for x. ​

Solve for x. ​ ​

given that f(x) = ln x. ​ f(x - 7) = f(x) - f(7), x > 0 ​

Evaluate the function at the indicated value of . ​ ​

$5500 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to double.(Approximate the result to two decimal places.) ​ ​

Select the graph of the exponential function. ​ ​ ​

Solve the exponential equation algebraically.Approximate the result to three decimal places. ​ ​

Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years.Of an initial sample of 33 grams, how much will remain after 69 years? ​

Select the graph of the function. ​ ​

Write the exponential equation in logarithmic form. ​ ​

Solve the equation algebraically.Round the result to three decimal places. ​ ​

Solve the exponential equation algebraically.Approximate the result to three decimal places. ​ ​

Use the properties of logarithms to simplify the expression. ​ ​

Which investment option will pay the most interest?

Condense the expression to the logarithm of a single quantity.

The populations P (in thousands) of Pittsburgh, Pennsylvania from 2000 through 2007 can be modeled by where t represents the year, with corresponding to 2000.Use the model to find the numbers of cell sites in the year 2009.

Rewrite the logarithm as a ratio of natural logarithms.

Use the One-to-One Property to solve the following equation for x.

Solve for x.

given that f(x) = ln x. f(x - 7) = f(x) - f(7), x > 0

Evaluate the function at the indicated value of .

$5500 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to double.(Approximate the result to two decimal places.)

Select the graph of the exponential function.

Solve the exponential equation algebraically.Approximate the result to three decimal places.

Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years.Of an initial sample of 33 grams, how much will remain after 69 years?

Select the graph of the function.

Write the exponential equation in logarithmic form.

Solve the equation algebraically.Round the result to three decimal places.

Solve the exponential equation algebraically.Approximate the result to three decimal places.

Use the properties of logarithms to simplify the expression.