College Algebra

Question

If a ball is dropped from a height of 576 ​feet, then its height in feet above the ground is given by h(t)=-16t^2 + 576 where t is in seconds. Find the average rate of change of the height of the ball as t varies from 4 to 6 seconds.

Answer 1

h(4) = -16*4^2 + 576 = 320

h(6) = -16*6^2 + 576 = 0

[ h(6) - h(4) ] / (6-4) =

-320/2 = -160

falls 160 feet per second

Answer 2

First, remember that the average rate of change = slope. We can find the slope when we have 2 points. While the problem didn't directly give us 2 points, we have all of the information needed to get them.

h(t) = -16t² + 576 --> h(t) is the same as y (just like f(x) = y)

We are also given t = 4 and t = 6, which is the equivalent of x here. If we plug in each of our t values into the equation given, we will get the corresponding y value and therefore will have our points.

For t = 4

h(4) = -16(4)² + 576 = 320

So our first point is (4, 320), and let's use this as (x₁, y₁)

For t = 6

h(6) = -16(6)² + 576 = 320

So our first point is (6, 0), and let's use this as (x₂, y₂)

Now to find the slope we can use:

m = (y₂ - y₁)/(x₂-x₁)

m = (0 - 320)/(6 - 4) = -320/2 = -160

The average rate of change of the height of the ball as t varies from 4 to 6 seconds is -160.