Question

The height in feet, h, of a model rocket t seconds after launch is given by the equation h(t) = 3+70t - 16t^2. The average rate of change in h(t) between t = 1 second and t = 3 second is 6. What does the average rate of change tell you about the rocket?​

Answer 1

The average rate of change

`(dh)/(d t) = 70 (1) - 16(2t)`

At t = 1

`(dh)/(d t) = 70 (1) - 16(2t) = 38`

at t=3



Explanation:

Step(I):-

The given function h(t) = 3+70t - 16t²

`(dh)/(d t) = 70 (1) - 16(2t)`

The
`(dh)/(d t) = 70 (1) - 16(2t) =0`

70 - 32 t = 0

⇒ 70 = 32 t

⇒
`t = (70)/(32) = (35)/(16)`

Step(ii):-

The average rate of change in h(t) between t = 1 second and t = 3 second

`(dh)/(d t) = 70 (1) - 16(2t)`

At t = 1

`(dh)/(d t) = 70 (1) - 16(2t) = 38`

At t = 3