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

Answer:

The average rate of change

$\frac{dh}{d t} = 70 (1) - 16(2t)$

At   t = 1

$\frac{dh}{d t} = 70 (1) - 16(2t) = 38$

at t=3



Step-by-step explanation:

Step(I):-

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

                          $\frac{dh}{d t} = 70 (1) - 16(2t)$

The       $\frac{dh}{d t} = 70 (1) - 16(2t) =0$

           70 - 32 t = 0

     ⇒   70 = 32 t

   ⇒     $t = \frac{70}{32} = \frac{35}{16}$

Step(ii):-

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

$\frac{dh}{d t} = 70 (1) - 16(2t)$

At   t = 1

$\frac{dh}{d t} = 70 (1) - 16(2t) = 38$

At t = 3