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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 + 32t + 90

The average rate of change of f(t) from t = 4 seconds to t = 6 seconds is :blank: feet per second.

Respuesta :

HomertheGenius
f ( 6 ) = -16·6²+32·6+90= -576 + 192 + 90 = -294
f ( 4 ) = -16· 4³+32·4+90=-256+128+90= -38
The average rate of change: [f(t2)-f(t1)]/ t2-t1=
[-294-(-38)] / (6-4) = -256 : 2 = -128 feet/s

The value of the average rate of change of f(t) is -128feet/s.

We have given that,

f(t) = −16t^2 + 32t + 90

f ( 6 ) = -16·6²+32·6+90= -576 + 192 + 90

f ( 6 ) = -294

f ( 4 ) = -16· 4³+32·4+90=-256+128+90

f ( 4 )= -38

What is the formula for the average rate of change?

The average rate of change

[tex][f(t_2)-f(t_1)]/ t_2-t_1[/tex]

Therefore by using the formula we get,

=[-294-(-38)] / (6-4)

= -256 / 2

= -128 feet/s

Therefore the value of the average rate of change of f(t) is -128feet/s.

To learn more about the average rate visit:

https://brainly.com/question/24313700

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