Question 1

Suppose a radioactive substance decays according to the formula   . How long will it take for the substance to decay to half the original amount?

Accepted Answer

A)  It will take 40 years for the substance to decay to half the original amount. 
B)  It will take 5,170 years for the substance to decay to half the original amount. 
C)  It will take 5,281 years for the substance to decay to half the original amount. 
D)  It will take 5,626 years for the substance to decay to half the original amount. 
A)  It will take 40 years for the substance to decay to half the original amount. 
B)  It will take 5,170 years for the substance to decay to half the original amount. 
C)  It will take 5,281 years for the substance to decay to half the original amount. 
D)  It will take 5,626 years for the substance to decay to half the original amount.

Question 2

Find the interest rate needed for an investment of $5,000 to grow to an amount of $6,000 in 3 year(s) if interest is compounded continuously. Round your answer to the nearest hundredth.
Interest rate is __________% per year.

Accepted Answer

The answer of Find the interest rate needed for an...

Question 3

During a flu epidemic, the number of children in the Woodbridge Community School System who contracted influenza after t days was given by   .
How many children were stricken by the flu after the first day? Round your answer to the nearest integer.
__________ children
How many children had the flu after 10 days? Round your answer to the nearest integer.
__________ children
How many children eventually contracted the disease? Round your answer to the nearest integer.
__________ children

Accepted Answer

The answer of During a flu epidemic, the number of...

Question 4

Use the definition of a logarithm to prove   .

Accepted Answer

By the def

Question 5

Use logarithmic differentiation to find the derivative of the function.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 6

Find the derivative of the function.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 7

Use the facts that log 3 = 0.4771 and log 4 = 0.6021 to find the value of the logarithm. Round your answer to four decimal places.
log 12

Accepted Answer

The answer of Use the facts that log 3 =...

Question 8

On the Richter scale, the magnitude   of an earthquake is given by the formula   where   is the intensity of the earthquake being measured and   is the standard reference intensity. Express the intensity   of an earthquake of magnitude   in terms of the standard intensity   .
Express the intensity   of an earthquake of magnitude   in terms of the standard intensity   .
How many times greater is the intensity of an earthquake of magnitude 7 than one of magnitude 5?
In modern times the greatest loss of life attributable to an earthquake occurred in eastern China in 1976. Known as the Tangshan earthquake, it registered 8.2 on the Richter scale. How does the intensity of this earthquake compare with the intensity of an earthquake of magnitude   ? Round your answer to the nearest integer.

Accepted Answer

A)    ;
  ; 2; 1,570 
B)    ;
  ; 100; 1,595 
C)    ;
  ; 100; 1,585 
D)    ;
  ; 100; 1,580 
A)    ;
  ; 2; 1,570 
B)    ;
  ; 100; 1,595 
C)    ;
  ; 100; 1,585 
D)    ;
  ; 100; 1,580

Question 9

Express the equation in logarithmic form.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 10

Find the derivative of the function.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 11

The height (in feet) of a certain kind of tree is approximated by   where   is the age of the tree in years. Estimate the age of a 90-ft tree. Round your answer to the nearest hundredth.
__________ years

Accepted Answer

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

Question 12

Use logarithms to solve the equation for t. Please round the answer to four decimal places.

Accepted Answer

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

Question 13

Express the equation in logarithmic form.

Accepted Answer

The answer of Express the equation in logarithmic form. ...

Question 14

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

Accepted Answer

A)    
B)    
C)    
A)    
B)    
C)

Question 15

Solve the equation for x.

Accepted Answer

A)  x = 7 
B)  x = 2 
C)  x = 16 
D)  x = 8 
A)  x = 7 
B)  x = 2 
C)  x = 16 
D)  x = 8

Question 16

Universal Instruments found that the monthly demand for its new line of Galaxy Home Computers t months after placing the line on the market was given by   . Select the graph of this function. At what level is the demand expected to stabilize?

Accepted Answer

A)    2,000 computers 
B)    1,900 computers 
C)    2,200 computers 
D)    2,000 computers 
E)    1,900 computers 
A)    2,000 computers 
B)    1,900 computers 
C)    2,200 computers 
D)    2,000 computers 
E)    1,900 computers

Question 17

Write the expression as the logarithm of a single quantity.

Accepted Answer

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

Question 18

Use the curve-sketching guideline, to select the graph of the function.

Accepted Answer

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

Question 19

Wood deposits recovered from an archeological site contain 25% of the carbon 14 they originally contained. How long ago did the tree from which the wood was obtained die? Hint: the decay constant k for carbon 14 is equal to 0.00012.

Accepted Answer

A)  The tree died 10,429 year(s) ago. 
B)  The tree died 11,552 year(s) ago. 
C)  The tree died 13,084 year(s) ago. 
D)  The tree died 8,096 year(s) ago. 
A)  The tree died 10,429 year(s) ago. 
B)  The tree died 11,552 year(s) ago. 
C)  The tree died 13,084 year(s) ago. 
D)  The tree died 8,096 year(s) ago.

Question 20

Use the facts that log 3 = 0.4771 to find the value of the logarithm.

Accepted Answer

A)  - 2.4771 
B)  - 2.9092 
C)  2.1629 
D)  - 2.3537 
A)  - 2.4771 
B)  - 2.9092 
C)  2.1629 
D)  - 2.3537

Suppose a radioactive substance decays according to the formula . How long will it take for the substance to decay to half the original amount?

Find the interest rate needed for an investment of $5,000 to grow to an amount of $6,000 in 3 year(s) if interest is compounded continuously. Round your answer to the nearest hundredth. Interest rate is __________% per year.

Use the definition of a logarithm to prove .

Use logarithmic differentiation to find the derivative of the function.

Find the derivative of the function.

Use the facts that log 3 = 0.4771 and log 4 = 0.6021 to find the value of the logarithm. Round your answer to four decimal places. log 12

Express the equation in logarithmic form.

Find the derivative of the function.

The height (in feet) of a certain kind of tree is approximated by where is the age of the tree in years. Estimate the age of a 90-ft tree. Round your answer to the nearest hundredth. __________ years

Use logarithms to solve the equation for t. Please round the answer to four decimal places.

Express the equation in logarithmic form.

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

Solve the equation for x.

Universal Instruments found that the monthly demand for its new line of Galaxy Home Computers t months after placing the line on the market was given by . Select the graph of this function. At what level is the demand expected to stabilize?

Write the expression as the logarithm of a single quantity.

Use the curve-sketching guideline, to select the graph of the function.

Wood deposits recovered from an archeological site contain 25% of the carbon 14 they originally contained. How long ago did the tree from which the wood was obtained die? Hint: the decay constant k for carbon 14 is equal to 0.00012.

Use the facts that log 3 = 0.4771 to find the value of the logarithm.

Preliminaries

Functions, Limits and the Derivative

Differentiation

Applications of the Derivative

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters

Exam 5: Exponential and Logarithmic Functions

Suppose a radioactive substance decays according to the formula . How long will it take for the substance to decay to half the original amount?

Find the interest rate needed for an investment of $5,000 to grow to an amount of $6,000 in 3 year(s) if interest is compounded continuously. Round your answer to the nearest hundredth. Interest rate is __________% per year.

Use the definition of a logarithm to prove .

Use logarithmic differentiation to find the derivative of the function.

Find the derivative of the function.

Use the facts that log 3 = 0.4771 and log 4 = 0.6021 to find the value of the logarithm. Round your answer to four decimal places. log 12

Express the equation in logarithmic form.

Find the derivative of the function.

The height (in feet) of a certain kind of tree is approximated by where is the age of the tree in years. Estimate the age of a 90-ft tree. Round your answer to the nearest hundredth. __________ years

Use logarithms to solve the equation for t. Please round the answer to four decimal places.

Express the equation in logarithmic form.

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

Solve the equation for x.

Universal Instruments found that the monthly demand for its new line of Galaxy Home Computers t months after placing the line on the market was given by . Select the graph of this function. At what level is the demand expected to stabilize?

Write the expression as the logarithm of a single quantity.

Use the curve-sketching guideline, to select the graph of the function.

Wood deposits recovered from an archeological site contain 25% of the carbon 14 they originally contained. How long ago did the tree from which the wood was obtained die? Hint: the decay constant k for carbon 14 is equal to 0.00012.

Use the facts that log 3 = 0.4771 to find the value of the logarithm.

Preliminaries

Functions, Limits and the Derivative

Differentiation

Applications of the Derivative

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters