Question 1

Three hundred students attended the dedication ceremony of a new building on a college campus. The president of the traditionally female college announced a new expansion program, which included plans to make the college coeducational. The number of students who learned of the new program t hours later is given by the function  .
If 600 students on campus had heard about the new program 2 hours after the ceremony, how many students had heard about the policy after 4 hours? __________
How fast was the news spreading 4 hours after the ceremony? Round the answer to the nearest integer. __________

Accepted Answer

The answer of Three hundred students attended the dedication ceremony...

Question 2

Find the present value of $70,000 due in 4 year(s) at the given rate of interest. Round your answers to the nearest dollar.
6% / year compounded monthly
$__________
9% / year compounded daily
$__________

Accepted Answer

The answer of Find the present value of $70,000 due...

Question 3

Evaluate the expression.

Accepted Answer

A)  27 
B)  24 
C)  2 
D)  3

Question 4

The height (in feet) of a certain kind of tree is approximated by  where t is the age of the tree in years. Estimate the age of a 70-ft tree. Please round the answer to two decimal places.  __________ years

Accepted Answer

The answer of The height (in feet) of a certain...

Question 5

The U.S. population is approximated by the function  , where P(t) is measured in millions of people and t is measured in 30-year intervals, with t = 0 corresponding to 1930. What is the expected population of the United States in 2050 (t = 4)? Round your answer to one decimal place.
__________ million

Accepted Answer

The answer of The U.S. population is approximated by the...

Question 6

The radioactive element polonium decays according to the law  , where  is the initial amount and the time t is measured in days. If the amount of polonium left after 420 days is 80 mg, what was the initial amount present?
__________ mg

Accepted Answer

The answer of The radioactive element polonium decays according to...

Question 7

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
The function  is continuous for all  .

Accepted Answer

The answer of Determine whether the statement is true or...

Question 8

Simplify the expression.

Accepted Answer

The answer of Simplify the expression. ...

Question 9

Use logarithmic differentiation to find the derivative of the function.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 10

Evaluate the expression.

Accepted Answer

A)  10 
B)  729 
C)  9 
D)  6

Question 11

Solve the equation for x.

Accepted Answer

The answer of Solve the equation for x. ...

Question 12

Find the accumulated amount A if the principal P is invested at an interest rate of r per year for t years. Round your answer to the nearest cent. P = $2,500, r = 6%, t = 15, compounded semiannually

Accepted Answer

A)  A = $6,108.05 
B)  A = $5,991.40 
C)  A = $6,068.16 
D)  A = $6,149.01

Question 13

Sketch the graphs of the given functions on the same axes.

Accepted Answer

A)   
B)   
C)

Question 14

The concentration of a drug in an organ at any time  (in seconds) is given by  where  is measured in grams/cubic centimeter  Round your answer to the nearest hundredth.
How long would it take for the concentration of the drug in the organ to reach 0.15  __________ seconds
How long would it take for the concentration of the drug in the organ to reach 0.12  __________ seconds

Accepted Answer

The answer of The concentration of a drug in an...

Question 15

Evaluate the expression.  = __________

Accepted Answer

The answer of Evaluate the expression.  = __________...

Question 16

Find the derivative of the function.

Accepted Answer

The answer of Find the derivative of the function. ...

Question 17

The change from religious to lay teachers at Roman Catholic schools has been partly attributed to the decline in the number of women and men entering religious orders. The percent of teachers who are lay teachers is given by  where t measured in decades, with  corresponding to the beginning of 1960.
What percent of teachers were lay teachers at the beginning of 1990? Please round the answer to one decimal place.
__________ %
How fast was the percent of lay teachers changing at the beginning of 1990? Please round the answer to two decimal places.
__________ % / year
Find the year when the percent of lay teachers was increasing most rapidly.

Accepted Answer

The answer of The change from religious to lay teachers...

Question 18

The concentration of a drug in an organ at any time t (in seconds) is given by  where  is measured in grams/cubic centimeter  . How long would it take for the concentration of the drug in the organ to reach 0.18  ? Please round the answer to two decimal places.

Accepted Answer

A)   sec 
B)   sec 
C)   sec 
D)   sec 
E)   sec

Question 19

Use the laws of logarithms to simplify the expression.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 20

Find an equation of the tangent line to the graph of  at its inflection point.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Exam 5: Exponential and Logarithmic Functions

Find the present value of $70,000 due in 4 year(s) at the given rate of interest. Round your answers to the nearest dollar. 6% / year compounded monthly $ 9% / year compounded daily $

Evaluate the expression.

The height (in feet) of a certain kind of tree is approximated by where t is the age of the tree in years. Estimate the age of a 70-ft tree. Please round the answer to two decimal places. __________ years

The radioactive element polonium decays according to the law , where is the initial amount and the time t is measured in days. If the amount of polonium left after 420 days is 80 mg, what was the initial amount present? __________ mg

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The function is continuous for all .

Simplify the expression.

Use logarithmic differentiation to find the derivative of the function.

Evaluate the expression.

Solve the equation for x.

Find the accumulated amount A if the principal P is invested at an interest rate of r per year for t years. Round your answer to the nearest cent. P = $2,500, r = 6%, t = 15, compounded semiannually

Sketch the graphs of the given functions on the same axes.

Evaluate the expression. = __________

Find the derivative of the function.

The concentration of a drug in an organ at any time t (in seconds) is given by where is measured in grams/cubic centimeter . How long would it take for the concentration of the drug in the organ to reach 0.18 ? Please round the answer to two decimal places.

Use the laws of logarithms to simplify the expression.

Find an equation of the tangent line to the graph of at its inflection point.

Exam 5: Exponential and Logarithmic Functions

Find the present value of $70,000 due in 4 year(s) at the given rate of interest. Round your answers to the nearest dollar. 6% / year compounded monthly $__________ 9% / year compounded daily $__________

Evaluate the expression.

The height (in feet) of a certain kind of tree is approximated by where t is the age of the tree in years. Estimate the age of a 70-ft tree. Please round the answer to two decimal places. __________ years

The radioactive element polonium decays according to the law , where is the initial amount and the time t is measured in days. If the amount of polonium left after 420 days is 80 mg, what was the initial amount present? __________ mg

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The function is continuous for all .

Simplify the expression.

Use logarithmic differentiation to find the derivative of the function.

Evaluate the expression.

Solve the equation for x.

Find the accumulated amount A if the principal P is invested at an interest rate of r per year for t years. Round your answer to the nearest cent. P = $2,500, r = 6%, t = 15, compounded semiannually

Sketch the graphs of the given functions on the same axes.

Evaluate the expression. = __________

Find the derivative of the function.

The concentration of a drug in an organ at any time t (in seconds) is given by where is measured in grams/cubic centimeter . How long would it take for the concentration of the drug in the organ to reach 0.18 ? Please round the answer to two decimal places.

Use the laws of logarithms to simplify the expression.

Find an equation of the tangent line to the graph of at its inflection point.

Find the present value of $70,000 due in 4 year(s) at the given rate of interest. Round your answers to the nearest dollar. 6% / year compounded monthly $ 9% / year compounded daily $