Question 1

​Write the equation of the line tangent to the curve   at the point (2,1). ​

Accepted Answer

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

Question 2

​The relationship between the number of decibels β and the intensity of a sound I in watts per square centimeter is given by   Find the rate of change in the number of decibels when the intensity is   watt per square centimeter.Round your answer to the nearest decibel.

Accepted Answer

A)  ​317 decibels per watt per square cm 
B)  ​25,645 decibels per watt per square cm 
C)  ​2,849 decibels per watt per square cm 
D)  ​230,802 decibels per watt per square cm 
E)  ​2,851 decibels per watt per square cm 
A)  ​317 decibels per watt per square cm 
B)  ​25,645 decibels per watt per square cm 
C)  ​2,849 decibels per watt per square cm 
D)  ​230,802 decibels per watt per square cm 
E)  ​2,851 decibels per watt per square cm

Question 3

Use a graphing utility to graph the function   ​ ​

Accepted Answer

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

Question 4

Suppose that the annual rate of inflation averages 4% over the next 10 years.With this rate of inflation,the approximate cost C of goods or services during any year in that decade will be given by   ,   where t is time in years and P is the present cost.If the price of an oil change for your car is presently $25.95,estimate the price 10 years from now.Round your answer to two decimal places.

Accepted Answer

A)  $39.95 
B)  $40.41 
C)  $41.95 
D)  $43.41 
E)  $38.41 
A)  $39.95 
B)  $40.41 
C)  $41.95 
D)  $43.41 
E)  $38.41

Question 5

​Find​     ​

Accepted Answer

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

Question 6

For   ,calculate   to three decimal places. ​

Accepted Answer

A)  1.609 
B)  24.142 
C)  7.828 
D)  0.600 
E)  4.828 
A)  1.609 
B)  24.142 
C)  7.828 
D)  0.600 
E)  4.828

Question 7

​Use the given information to write an exponential equation for y.Does the function represent exponential growth or exponential decay? ​   ,when

Accepted Answer

A)  ​   , exponential decay 
B)  ​   , exponential growth 
C)  ​   , exponential decay 
D)  ​   , exponential growth 
A)  ​   , exponential decay 
B)  ​   , exponential growth 
C)  ​   , exponential decay 
D)  ​   , exponential growth

Question 8

​Sketch the graph of the function   ​

Accepted Answer

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

Question 9

​Simplify   ​

Accepted Answer

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

Question 10

​Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 11

​A survey of high school seniors from a certain school district who took the SAT has determined that the mean score on the mathematics portion was 500 with a standard deviation of 15.5.Assuming the data can be modeled by a normal probability density function,find a model for these data.

Accepted Answer

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

Question 12

​Find   if   ​

Accepted Answer

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

Question 13

​The average time between incoming calls at a switchboard is 3 minutes.If a call has just come in,the probability that the next call will come within the next t minutes is   Find the probability that the next call will come within the next   minute.Round your answer to two decimal places.

Accepted Answer

A)  ​24.25% 
B)  ​2.43% 
C)  ​175.75% 
D)  ​26.48% 
E)  ​5.97% 
A)  ​24.25% 
B)  ​2.43% 
C)  ​175.75% 
D)  ​26.48% 
E)  ​5.97%

Question 14

​Solve the exponential equation.Give the answer correct to 3 decimal places. ​   ​

Accepted Answer

A)  ​0.675 
B)  ​3.374 
C)  ​7.410 
D)  ​0.599 
E)  ​14.979 
A)  ​0.675 
B)  ​3.374 
C)  ​7.410 
D)  ​0.599 
E)  ​14.979

Question 15

​If   ,find   ​

Accepted Answer

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

Question 16

​Find the equation of the tangent line to   at the point   ​

Accepted Answer

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

Question 17

​Solve   for t.Round your answer to four decimal places. ​

Accepted Answer

A)  ​1.4454 
B)  ​0.3611 
C)  ​2.6344 
D)  ​0.3614 
E)  ​2.7184 
A)  ​1.4454 
B)  ​0.3611 
C)  ​2.6344 
D)  ​0.3614 
E)  ​2.7184

Question 18

​Use a calculator to evaluate the logarithm   Round your answer to three decimal places.

Accepted Answer

A)  ​0.195 
B)  ​2.464 
C)  ​6.402 
D)  ​3.737 
E)  ​5.129 
A)  ​0.195 
B)  ​2.464 
C)  ​6.402 
D)  ​3.737 
E)  ​5.129

Question 19

​Find the derivative of the function

Accepted Answer

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

Question 20

Use the properties of exponents to simplify the expression   ​

Accepted Answer

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

Write the equation of the line tangent to the curve at the point (2,1).

The relationship between the number of decibels β and the intensity of a sound I in watts per square centimeter is given by Find the rate of change in the number of decibels when the intensity is watt per square centimeter.Round your answer to the nearest decibel.

Use a graphing utility to graph the function

Find

For ,calculate to three decimal places.

Use the given information to write an exponential equation for y.Does the function represent exponential growth or exponential decay? ,when

Sketch the graph of the function

Simplify

Find the derivative of the following function.

A survey of high school seniors from a certain school district who took the SAT has determined that the mean score on the mathematics portion was 500 with a standard deviation of 15.5.Assuming the data can be modeled by a normal probability density function,find a model for these data.

Find if

The average time between incoming calls at a switchboard is 3 minutes.If a call has just come in,the probability that the next call will come within the next t minutes is Find the probability that the next call will come within the next minute.Round your answer to two decimal places.

Solve the exponential equation.Give the answer correct to 3 decimal places.

If ,find

Find the equation of the tangent line to at the point

Solve for t.Round your answer to four decimal places.

Use a calculator to evaluate the logarithm Round your answer to three decimal places.

Find the derivative of the function

Use the properties of exponents to simplify the expression

Functions, graphs, and Limits

Differentiation

Applications of the Derivative

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

Exam 4: Exponential and Logarithmic Functions

​Write the equation of the line tangent to the curve at the point (2,1). ​

​The relationship between the number of decibels β and the intensity of a sound I in watts per square centimeter is given by Find the rate of change in the number of decibels when the intensity is watt per square centimeter.Round your answer to the nearest decibel.

Use a graphing utility to graph the function ​ ​

​Find​ ​

For ,calculate to three decimal places. ​

​Use the given information to write an exponential equation for y.Does the function represent exponential growth or exponential decay? ​ ,when

​Sketch the graph of the function ​

​Simplify ​

​Find the derivative of the following function. ​ ​

​A survey of high school seniors from a certain school district who took the SAT has determined that the mean score on the mathematics portion was 500 with a standard deviation of 15.5.Assuming the data can be modeled by a normal probability density function,find a model for these data.

​Find if ​

​The average time between incoming calls at a switchboard is 3 minutes.If a call has just come in,the probability that the next call will come within the next t minutes is Find the probability that the next call will come within the next minute.Round your answer to two decimal places.

​Solve the exponential equation.Give the answer correct to 3 decimal places. ​ ​

​If ,find ​

​Find the equation of the tangent line to at the point ​

​Solve for t.Round your answer to four decimal places. ​

​Use a calculator to evaluate the logarithm Round your answer to three decimal places.

​Find the derivative of the function

Use the properties of exponents to simplify the expression ​

Functions, graphs, and Limits

Differentiation

Applications of the Derivative

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

Write the equation of the line tangent to the curve at the point (2,1).

The relationship between the number of decibels β and the intensity of a sound I in watts per square centimeter is given by Find the rate of change in the number of decibels when the intensity is watt per square centimeter.Round your answer to the nearest decibel.

Use a graphing utility to graph the function

Find

For ,calculate to three decimal places.

Use the given information to write an exponential equation for y.Does the function represent exponential growth or exponential decay? ,when

Sketch the graph of the function

Simplify

Find the derivative of the following function.

A survey of high school seniors from a certain school district who took the SAT has determined that the mean score on the mathematics portion was 500 with a standard deviation of 15.5.Assuming the data can be modeled by a normal probability density function,find a model for these data.

Find if

The average time between incoming calls at a switchboard is 3 minutes.If a call has just come in,the probability that the next call will come within the next t minutes is Find the probability that the next call will come within the next minute.Round your answer to two decimal places.

Solve the exponential equation.Give the answer correct to 3 decimal places.

If ,find

Find the equation of the tangent line to at the point

Solve for t.Round your answer to four decimal places.

Use a calculator to evaluate the logarithm Round your answer to three decimal places.

Find the derivative of the function

Use the properties of exponents to simplify the expression