The height in feet, h , of a model rocket t seconds after launch is given by the equation h of t is equal to 3 plus 70 t minus 16 t squared The average rate of change in h of t between t is equal to 1 second and t is equal to 3 second is 6 What does the average rate of change tell you about the rocket?
Answer
A
The rocket is 6 feet higher above the ground when t is equal to 3 than it is when t is equal to 1 .
B
The rocket is at a greater height when t is equal to 3 than it is when t is equal to 1 .
C
The rocket is traveling at a constant rate of 6 feet per second between t is equal to 1 and t is equal to 3 .
D
The rocket is traveling six times as fast when t is equal to 3 than it is when t is equal to 1 .
Explanation
The average rate of change is the change in height divided by the change in time. From 1 to 3 seconds, the time interval is 2 seconds, so an average rate of 6 feet per second means the rocket’s height increases by 6 × 2 = 12 feet. Thus, the rocket is at a greater height at 3 seconds than at 1 second; it does not travel at a constant rate.
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