Question

The height in feet, h, of a model rocket t seconds after launch is given by the equation h (t) = 3 + 70 t minus 16 t squared. 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

Kindly check explanation

Explanation:

Given the model equation:

h (t) = 3 + 70t - 16t²

h = height in feet

t = time in seconds

Average rate of change in h(t) between

t= 1 second and t = 3 second

At t = 1 second

h(1) = 3 + 70(1) - 16(1)^2 = 57

At t = 3 second

h(3) = 3 + 70(3) - 16(3)^2 = 69

Average rate of change = Δh / Δt

Δh / ΔT = [h(3) - h(1)] / (3 - 1)

= (69 - 57) / 2

= 12 / 2

= 6

Hence, it is the mean or average change in height h as time, t changes