Question

24. The function f(t) = -16t^2 +20t +4 gives the height of a ball, in feet, t seconds after it is tossed.

Answer 1

Answer:

-12 feet per second

Step-by-step explanation:

average rate of change over [0.75, 1.25] = $\frac{f(1.25) - f(0.75)}{1.25 - 0.75}$

f(1.25) - f(0.75) = 4 - 10 = -6

1.25 - 0.75 = 0.5

$\frac{f(1.25) - f(0.75)}{1.25 - 0.75}$ = $\frac{-6}{0.5}$ = -12

Answer 2

Answer:

-16feet/second

Step-by-step explanation:

If the height or the ball is modelled nu the equation f(t) = -16t^2 +20t +4

The average rate of change is the velocity of the ball.

Velocity = {d(f(t)}/dt = -32t+20

The velocity of the ball over the interval [0.75, 1.25] can be gotten by taken the difference of the velocity at t = 0.75 from when t = 1.25

f'(t) = -32t+20

f'(0.75) = -32(0.75)+20

f'(0.75) = -24+20

f'(0.75) = -4ft/s

At t = 1.25s

f'(1.25) = -32(1.25)+20

f'(1.25) = -40+20

f'(1.25) = -20ft/s

Rate of change = f'(1.25) - f'(0.75)

Rate of change in height = -20-(-4)

Rate of change in height = -16ft/s