Question

Your friend drops a rubber ball from 4ft. 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

Answer 1

To model the height of the rubber ball as it bounces, an exponential function can be used. The decreasing exponential function can be represented as y = a * b^x, where a represents the initial height and b represents the bounce factor.

Step-by-step explanation:

To model the height of the rubber ball as it bounces, we can use an exponential function. In this case, since the height decreases with each bounce, we would use a decreasing exponential function.

A general form of a decreasing exponential function is: y = a * b^x, where a represents the initial height and b represents the bounce factor.

Let's use the given information to determine the values of a and b. From the first bounce, we have: 32.5 = a * b^1. From the second bounce, we have: 22 = a * b^2.

By substituting the values we can solve for a and b to find the exponential function that models the height of the ball.