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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)=-16t^2+48t+100 the average rate of change of f(t) from t=3 seconds to t= 5 seconds is feet per seconds

Respuesta :

Hi,
Avg rate of change formula is

Avg(rate of change)=F[tex] x_{2}- x_{1} / t_{2} - t_{1} [/tex]

we need to put t's value in function
put t=5
f(5)=-16(5)^2+48(5)+100
f(5)=-400+240+100
f(5)=-60



we put t=3 now

f(3)=-16(3)^2+48*3+100

f(3)=100

Avg(rate of change)=100-(-6)/5-3
100+60/2
160/2
80

then Avg(rate of change is 80

apologiabiology
easy,

height is ouput
time is input
feet per second
average over that time

so basically (change in height)/(change in time) or

[tex] \frac{f(5)-f(3)}{5-3} [/tex]
just like slope
that is what we are doint, we are finding the slope between those points
so
f(3)=100
f(5)=-60

[tex] \frac{f(5)-f(3)}{5-3} [/tex]=[tex] \frac{-60-100}{2} [/tex]=[tex] \frac{-160}{2} [/tex]=-80

average rate of change is -80ft/sec

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