Begin by writing ordered pairs by looking at the table.
B
b
The average rate of change can be found by dividing the change in height by the change in time.
C
c
The average rate of change can be found by dividing the change in height by the change in time.
D
d
What is the unit of the rate of change?
A
a
B
b
-30 ft/s
C
c
-24 ft/s
D
d
Speed
Practice makes perfect
a
The table shows the height on a water slide at various time intervals.
Time (s)
Height (ft)
0
120
1
90
2
60
3
30
4
0
5
0
To graph the height versus time, let the y-axis represent the height and the x-axis represent the time. Then, we can write an ordered pair for each time interval.
(0,120), (1,90), (2,60),
(3,30), (4,0), (5,0)
Now we can plot these points on the coordinate plane.
b
To find the average rate of change in the rider's height, we will use a formula.
average rate of change&=change in y/change in x [1.2em]
&=change in height/change in timeLet's first find the change in height and time.
change in height:& 30-90=-60
change in time:& 3-1=2
Now we can find the average rate of change.
average rate of change&=-60/2=-30
The average rate of change of a rider between 1 and 3 seconds is -30 ft/s.
c
We will find the average rate of change between 0 and 5 seconds as we did in Part B.
change in height:& -120=-120
change in time:& 5- =5
Now we can find the rate of change.
average rate of change&=-120/5=-24
Thus, the average rate of change is -24 ft/s.
d
Since the unit of the average rate of change is ft/s, the word is speed.
