Question

A ball is dropped from a height of 50 inches. The height of the ball after each bounce is half the height the ball reached on the previous bounce. You can use a function to describe the height the ball reaches after x bounces.
Write an equation for the function. If it is linear, write it in the form h(x)=mx+b. If it is exponential, write it in the form h(x)=a(b)x.

Answer 1

The heights form a geometric sequence (each bounce reaches half the previous), so the function is exponential:

h(x) = 50(1/2)^x, for x = 0, 1, 2, 3, ...

(Here h(0)=50 inches, h(1)=25 inches, h(2)=12.5 inches, etc.)