Question 1

Evaluate the integral below. Use a graphing calculator to check your answer.

Accepted Answer

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

Question 2

Blood pressure varies for individuals throughout the course of a day, typically being the lowest at night and the highest from late morning to early afternoon. The estimated rate of change in diastolic blood pressure for a patient with untreated hypertension is shown in the table. Find a model, B(t) for the data, where t is the number of hours since 8 A.M.

Accepted Answer

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

Question 3

The acceleration of a race car during the first 25 seconds of a road test is modeled by   where t is the number of seconds since the test began. Assume the velocity and distance were both zero at the beginning of the road test. Calculate, to three decimal places, the average acceleration during the first 25 seconds of the road test.

Accepted Answer

A)  1.150 ft/sec2 
B)  5.695 ft/sec2 
C)  19.930 ft/sec2 
D)  4.445 ft/sec2 
E)  13.680 ft/sec2 
A)  1.150 ft/sec2 
B)  5.695 ft/sec2 
C)  19.930 ft/sec2 
D)  4.445 ft/sec2 
E)  13.680 ft/sec2 B

Question 4

Consider the graph of r(t), the rate of change in the price of a technology stock, during the first 55 days of trading of 2003. Using the information present below, find the graph of the accumulation function starting at day 16.

Accepted Answer

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

Question 5

If possible, find the general antiderivative of   .

Accepted Answer

A)  There is no general antiderivative. 
B)    
C)    
D)    
E)    
A)  There is no general antiderivative. 
B)    
C)    
D)    
E)

Question 6

Find   .

Accepted Answer

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

Question 7

The federal government standard says that carbon monoxide (CO) levels should not exceed 35-ppm (parts per million) at any time. The concentration of carbon monoxide in the air in a certain metropolitan area can be modeled as   ppm h hours after 7 A.M. Did the city exceed the 35-ppm maximum in the 8 hours between 7 A.M. and 3 P.M? If the answer is yes, give the time when the city first exceeded the 35-ppm maximum.

Accepted Answer

A)  No. 
B)  Yes, around 8:30 A.M. 
C)  Yes, around 11 A.M. 
D)  Yes, around noon. 
E)  Yes, around 1:30 P.M. 
A)  No. 
B)  Yes, around 8:30 A.M. 
C)  Yes, around 11 A.M. 
D)  Yes, around noon. 
E)  Yes, around 1:30 P.M.

Question 8

Evaluate the integral   .

Accepted Answer

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

Question 9

A program to protect a species of endangered bird is to be phased out by the year 2020. An environmental group has projected the rate of change in the bird population between 2000 and 2020 as shown in the figure below.   Given that projection, what will a graph of the bird population between 2000 and 2050 look like, using the the following information:   At the beginning of 2000 there were 1.1 million birds in existence.   The species will be extinct by 2050.

Accepted Answer

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

Question 10

The graph of   represents the rate of change of rainfall during a severe thunderstorm t hours after rainfall began. Draw a graph of the total amount of rain that fell during this storm, using the following facts:   The rainfall started at 2 P.M. and did not stop until 8 P.M.   2 inches of rain fell between 2 P.M. and 5 P.M.   The total amount of rain that fell during the storm was 5.2 inches.

Accepted Answer

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

Question 11

Scientists can model the change in snow depth per day. The graph below shows a model using equivalent centimeters of water per day form April 1 to June 9. Estimate, to the nearest centimeter, the area of the region beneath the curve from May 12 (day 42) to June 9 (day 70). Interpret your answer.

Accepted Answer

A)  Between May 12 (day 42) and June 9 (day 70), there was snowfall equivalent to approximately 3 centimeters of water. 
B)  Between May 12 (day 42) and June 9 (day 70), there was snowfall equivalent to approximately 5 centimeters of water. 
C)  Between May 12 (day 42) and June 9 (day 70), each day there was snowfall equivalent to approximately 5 centimeters of water. 
D)  Between May 12 (day 42) and June 9 (day 70), each day there was snowfall equivalent to approximately 3 centimeters of water. 
E)  Between May 12 (day 42) and June 9 (day 70), there was snowfall equivalent to approximately 2 centimeters of water. 
A)  Between May 12 (day 42) and June 9 (day 70), there was snowfall equivalent to approximately 3 centimeters of water. 
B)  Between May 12 (day 42) and June 9 (day 70), there was snowfall equivalent to approximately 5 centimeters of water. 
C)  Between May 12 (day 42) and June 9 (day 70), each day there was snowfall equivalent to approximately 5 centimeters of water. 
D)  Between May 12 (day 42) and June 9 (day 70), each day there was snowfall equivalent to approximately 3 centimeters of water. 
E)  Between May 12 (day 42) and June 9 (day 70), there was snowfall equivalent to approximately 2 centimeters of water.

Question 12

The rate of change of the weight of a laboratory mouse can be modeled by the equation   grams per week where t is the age of the mouse in weeks and   .
Use limit of sums to estimate   .

Accepted Answer

A)  17.9 grams 
B)  7.8 grams 
C)  0.8 grams 
D)  13.8 grams 
E)  37.3 grams 
A)  17.9 grams 
B)  7.8 grams 
C)  0.8 grams 
D)  13.8 grams 
E)  37.3 grams

Question 13

Find the specific antiderivative of   .

Accepted Answer

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

Question 14

Consider the graph of f(t).   What does the graph of the accumulation function   look like?

Accepted Answer

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

Question 15

Consider the graph of r(t), the rate of change in the price of a technology stock, during the first 55 days of trading of 2003. Using the information present below, fill in the accumulation function values in the accompanying table.

Accepted Answer

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

Question 16

The acceleration of a race car during the first 35 seconds of a road test is modeled by   where t is the number of seconds since the test began. Assume the velocity and distance were both zero at the beginning of the road test. Calculate, to three decimal places, the average velocity during the first 35 seconds of the road test.

Accepted Answer

A)  120.021 ft/sec 
B)  169.021 ft/sec 
C)  0.005 ft/sec 
D)  1.258 ft/sec 
E)  386.750 ft/sec 
A)  120.021 ft/sec 
B)  169.021 ft/sec 
C)  0.005 ft/sec 
D)  1.258 ft/sec 
E)  386.750 ft/sec

Question 17

The cost of producing x units of a certain item is   Find the average value of the cost function C(x) over the interval from 0 to 1000. Round answer to nearest penny.

Accepted Answer

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

Question 18

Suppose the population of a country between 1921 and 2000 is given by the model Population   million people
Where t is the number of years since the end of 1900. What was the average population of the country from the beginning of 1990 through the end of 1999? Round your answer to the nearest tenth.

Accepted Answer

A)  90.5 million people 
B)  89.8 million people 
C)  39.3 million people 
D)  90.0 million people 
E)  88.8 million people 
A)  90.5 million people 
B)  89.8 million people 
C)  39.3 million people 
D)  90.0 million people 
E)  88.8 million people

Question 19

Find the area of the shaded region.

Accepted Answer

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

Question 20

Consider the graph of f(t).   What does the graph of the accumulation function   look like?

Accepted Answer

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

Evaluate the integral below. Use a graphing calculator to check your answer.

Consider the graph of r(t), the rate of change in the price of a technology stock, during the first 55 days of trading of 2003. Using the information present below, find the graph of the accumulation function starting at day 16.

If possible, find the general antiderivative of .

Find .

Evaluate the integral .

Scientists can model the change in snow depth per day. The graph below shows a model using equivalent centimeters of water per day form April 1 to June 9. Estimate, to the nearest centimeter, the area of the region beneath the curve from May 12 (day 42) to June 9 (day 70). Interpret your answer.

The rate of change of the weight of a laboratory mouse can be modeled by the equation grams per week where t is the age of the mouse in weeks and . Use limit of sums to estimate .

Find the specific antiderivative of .

Consider the graph of f(t). What does the graph of the accumulation function look like?

Consider the graph of r(t), the rate of change in the price of a technology stock, during the first 55 days of trading of 2003. Using the information present below, fill in the accumulation function values in the accompanying table.

The cost of producing x units of a certain item is Find the average value of the cost function C(x) over the interval from 0 to 1000. Round answer to nearest penny.

Suppose the population of a country between 1921 and 2000 is given by the model Population million people Where t is the number of years since the end of 1900. What was the average population of the country from the beginning of 1990 through the end of 1999? Round your answer to the nearest tenth.

Find the area of the shaded region.

Consider the graph of f(t). What does the graph of the accumulation function look like?

Ingredients of Change: Functions an Limits

Describing Change: Rates

Determining Change: Derivatives

Analyzing Change: Applications of Derivatives

Analyzing Accumulated Change: Integrals in Action

Ingredients of Multivariable Change: Models, Graphs, Rates

Analyzing Multivariable Change: Optimization

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Exam 5: Accumulating Change: Limits of Sums and the Definite Integral

Evaluate the integral below. Use a graphing calculator to check your answer.

Consider the graph of r(t), the rate of change in the price of a technology stock, during the first 55 days of trading of 2003. Using the information present below, find the graph of the accumulation function starting at day 16.

If possible, find the general antiderivative of .

Find .

Evaluate the integral .

Scientists can model the change in snow depth per day. The graph below shows a model using equivalent centimeters of water per day form April 1 to June 9. Estimate, to the nearest centimeter, the area of the region beneath the curve from May 12 (day 42) to June 9 (day 70). Interpret your answer.

The rate of change of the weight of a laboratory mouse can be modeled by the equation grams per week where t is the age of the mouse in weeks and . Use limit of sums to estimate .

Find the specific antiderivative of .

Consider the graph of f(t). What does the graph of the accumulation function look like?

Consider the graph of r(t), the rate of change in the price of a technology stock, during the first 55 days of trading of 2003. Using the information present below, fill in the accumulation function values in the accompanying table.

The cost of producing x units of a certain item is Find the average value of the cost function C(x) over the interval from 0 to 1000. Round answer to nearest penny.

Suppose the population of a country between 1921 and 2000 is given by the model Population million people Where t is the number of years since the end of 1900. What was the average population of the country from the beginning of 1990 through the end of 1999? Round your answer to the nearest tenth.

Find the area of the shaded region.

Consider the graph of f(t). What does the graph of the accumulation function look like?

Ingredients of Change: Functions an Limits

Describing Change: Rates

Determining Change: Derivatives

Analyzing Change: Applications of Derivatives

Analyzing Accumulated Change: Integrals in Action

Ingredients of Multivariable Change: Models, Graphs, Rates

Analyzing Multivariable Change: Optimization

Filters