Question

A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, f(t), in feet, at different times, t, in seconds: f(t) = −16t2 + 34t + 80 The average rate of change of f(t) from t = 5 seconds to t = 7 seconds is _____ feet per second.

Answer 1

at t = 5 second f(t) = -16*25 + 34*5+ 80 = -150

and at t = 7 seconds f(t) = -16*49 + 34*7 + 80 = -466

average rate of change = (-466 - (-150) / 7 - 5 = -158 feet / second

Answer 2

The average rate of change is -158 feet per second.

Explanation:

Given : A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, f(t), in feet, at different times, t, in seconds :
`f(t) = -16t^2 + 34t + 80`

To find : The average rate of change of f(t) from t = 5 seconds to t = 7 seconds ?

Solution :

First we find the value of f(t) at t=5 and t=7

At t=5 seconds

`f(t) = -16t^2 + 34t + 80`

`f(t) = -16(5)^2 + 34(5)+ 80`

`f(t) = -16(25) + 170+ 80`

`f(t) = -400+250`

`f(t) = -150`

At t=7 seconds

`f(t) = -16t^2 + 34t + 80`

`f(t) = -16(7)^2 + 34(7)+ 80`

`f(t) = -16(49) +238+ 80`

`f(t) = -784+318`

`f(t) = -466`

The average rate of change is

`m=(y_2-y_1)/(x_2-x_1)`

`m=(f(7)-f(5))/(7-5)`

`m=(-466-(-150))/(2)`

`m=(-316)/(2)`

`m=-158`

Therefore, The average rate of change is -158 feet per second.