Question

27. Your friend drops a rubber ball from 4 ft. You notice that its rebound is 32.5
in. on the first bounce and 22 in. on the second bounce.
a. What exponential function would be a good model for the height of the
ball?
b. How high will the ball bounce on the fourth bounce?

Answer 1

a. We can model the height of the ball using the exponential function h(n) = h0 * r^n, where h0 is the initial height, r is the rebound ratio, and n is the bounce number.

From the information given:
h(0) = 4 ft = 48 in
h(1) = 32.5 in
h(2) = 22 in

Using the values for the first two bounces to find the rebound ratio:
32.5 = 48 * r
r = 32.5 / 48 = 0.677

Now we can write the function for the height of the ball:
h(n) = 48 * 0.677^n

b. To find the height on the fourth bounce, we calculate h(3):
h(3) = 48 * 0.677^3 ≈ 20.4 in

Therefore, the ball will bounce approximately 20.4 inches on the fourth bounce.