1.
Find the average value of over .

Answer:


2.
Find the average value of over .

Answer:


3.
Consider the function whose graph is given below.

Find

Answer:


4.
Consider the function whose graph is given below.

What is the average value of on ?

Answer:


5.
Consider the function graphed below.

Estimate

Answer:


6.
Consider the function graphed below.

Which of the following average values of is larger?
A.
Between and
B.
Between and


7.
The following table gives the emissions, , of nitrogen oxides in millions of metric tons per year in the US. Let be the number of years since and .
Year
1940
1950
1960
1970
1980
1990

Estimate

Answer:


8.
The amount of waste a company produces, , in metric tons per week, is approximated by , where is in weeks since January 1, . Waste removal for the company costs $ton. How much does the company pay for waste removal during the year ? Omit the dollar sign from your answer.

Answer:


9.
A two-day environmental clean up started at 9 am on the first day. The number of workers fluctuated as shown below.

If the workers were paid $10 per hour, how much was the total personnel cost of the clean up? Omit the dollar sign from your answer.

Answer:


10.
A two-day environmental clean up started at 9 am on the first day. The number of workers fluctuated as shown below.

Suppose that the workers were paid $10 per hour for work during the time period 9 am to 5 pm and were paid $15 per hour for work during the rest of the day. What would the total personnel costs of the clean up have been under these conditions? Omit the dollar sign from your answer.

Answer:


11.
A warehouse charges its customers $5 per day for every cubic feet of space used for storage. The figure records the storage used by one company over a month. How much will the company have to pay?
Omit the dollar sign from your answer.

Answer:


12.
A bar of metal is cooling from C to room temperature, C. The temperature, , of the bar minutes after it starts cooling is given, in C, by


Find the temperature of the bar at the end of one hour.

Answer:


13.
A bar of metal is cooling from C to room temperature, C. The temperature, , of the bar minutes after it starts cooling is given, in C, by


Find the average value of the temperature over the first hour.

Answer:


14.
The number of hours, , of daylight in Madrid as a function of date is approximated by the formula
where is the number of days since the start of the year.

Find the average number of hours of daylight in Madrid in January.

Answer:


15.
The number of hours, , of daylight in Madrid as a function of date is approximated by the formula
where is the number of days since the start of the year.

Find the average number of hours of daylight in Madrid in June.

Answer:


16.
The number of hours, , of daylight in Madrid as a function of date is approximated by the formula
where is the number of days since the start of the year.

Find the average number of hours of daylight in Madrid over a year.

Answer:


17.
For the even function in the figure, consider the average value of over the following intervals:
, , ,

For which interval is the average value of least?
A.
I
B.
II
C.
III
D.
IV


18.
For the even function in the figure, consider the average value of over the following intervals:
, , ,

For which interval is the average value of greatest?
A.
I
B.
II
C.
III
D.
IV


19.
For the even function in the figure, consider the average value of over the following intervals:
, , ,

For which pair of intervals are the average values equal?
A.
I
B.
II
C.
III
D.
IV


20.
Coal gas is produced at a gasworks. Pollutants in the gas are removed by scrubbers, which become less and less efficient as time goes on. The following measurements, made at the start of each month, show the rate at which pollutants are escaping (in tons/month) in the gas:
Time (months)
Rate pollutants escape


Make an overestimate and an underestimate of the total quantity of pollutants that escape during the first six months. [Separate your answers with a semicolon].

Answer:



STOP This is the end of the test. When you have completed all the questions and reviewed your answers, press the button below to grade the test.