Review for 9.1 Quiz
Name: ________________________________
Directions: Complete these problems on a separate sheet of paper.
Lessons 9.1.1 and 9.1.2 Rates of Change From Data
1.
The amount of money in a bank account at the end of each month is given in the table below.
time (months)
balance ($)
2.
0
507
1
1276
3
1104
6
1353
a.
Calculate the average change in the balance for each given interval.
b.
How would the average rate of change relate to a graph of the data?
9
987
12
1074
The table below shows the amount of carbon emissions (in million tons) worldwide for the given years. Enter the
data into your calculator and create a plot of the data.
Year
1950
1955
1960
1965
1970
Emissions
1620
2020
2543
3095
4006
Year
1975
1980
1985
1988
1990
Emissions
4527
5170
5286
5809
5943
Year
1992
1993
1994
1995
Emissions
5926
5919
5989
6080
Find the average rate of change between :
a.
b.
c.
d.
e.
1950 and 1960
1960 and 1970
1970 and 1980
1980 and 1990
1990 and 1995.
3. A person who is running takes their heart rate at certain times during their workout. The data they collected is
recorded in the table below.
time (min)
heart rate
(beats per min.)
0
15
20
25
27
28
30
85
135
155
170
175
162
130
a.
Calculate the average change in heart rate for each interval.
b.
As the heart rate increases, what is happening to the change in heart rate? How is this represented on the
graph?
c.
Write a scenario to describe the data.
Lessons 9.1.3 and 9.1.4 Slope, Average Velocity, and Rates of Change
1.
2.
A car travels such that its distance from home is d(t)  3t 2  2 miles for t  1 to t  7 hours of travel.
a.
Calculate the average rate of change for each 1-hour interval.
b.
Use the information from part (a) to find a formula for the velocity of the car at any time t.
A ball is thrown off the top of a building and lands on the ground below. The function h(t)  16t 2  64t  48
gives the ball’s height in feet with respect to time in seconds.
3.
a.
When will the ball hit the ground?
b.
Make a table of time versus height. Use 1-second increments. Use the table to sketch a graph of the function
over the interval that fits this situation.
c.
Find the average velocity for each 1-second time interval that the ball is in the air.
d.
What is happening to the average velocity of the ball with respect to the time?
e.
What does the average velocity tell you about the change in position of the ball?
A rocket is launched off of a platform such that its height is determined by the function h(t)  16t 2  128t  4 ,
where time is in seconds.
a.
When will the rocket hit the ground?
b.
Make a table of time versus height. Use 1-second increments. Use the table to sketch a graph of the function
over the interval that fits this situation.
c.
Find the average velocity for each 1-second time interval that the ball is in the air.
d.
What is happening to the average velocity of the ball with respect to the time?
e.
What does the average velocity tell you about the change in position of the ball?
4.
Determine the average rate of change for the function 2x 2  x between x  3 and x  3  h . Simplify your
answer completely.
5.
Determine the average rate of change for the function f (x)  x 2  6x between x  2 and x  2  h . Simplify
your answer completely.
6.
Determine the average rate of change for the function f (x)  1x  2x between x  5 and x  5  h . Simplify
your answer completely.
7.
A man standing on a bridge drops a coin into a water fountain from a height of 105 ft. The height of the coin with
respect to time is given by the function h(t)  105  16t 2 , where t is in seconds and t  0 . Find the average
speed of the coin for the first 2 seconds after it is dropped. What is the average speed of the coin between 2 seconds
and the time it takes to hit the water?