Respuesta :
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
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:
The average rate of change is -158 feet per second.
Step-by-step 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 : [tex]f(t) = -16t^2 + 34t + 80[/tex]
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
[tex]f(t) = -16t^2 + 34t + 80[/tex]
[tex]f(t) = -16(5)^2 + 34(5)+ 80[/tex]
[tex]f(t) = -16(25) + 170+ 80[/tex]
[tex]f(t) = -400+250[/tex]
[tex]f(t) = -150[/tex]
At t=7 seconds
[tex]f(t) = -16t^2 + 34t + 80[/tex]
[tex]f(t) = -16(7)^2 + 34(7)+ 80[/tex]
[tex]f(t) = -16(49) +238+ 80[/tex]
[tex]f(t) = -784+318[/tex]
[tex]f(t) = -466[/tex]
The average rate of change is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{f(7)-f(5)}{7-5}[/tex]
[tex]m=\frac{-466-(-150)}{2}[/tex]
[tex]m=\frac{-316}{2}[/tex]
[tex]m=-158[/tex]
Therefore, The average rate of change is -158 feet per second.
