Question

suppose you drop a tennis ball from a height of 14 feet. After the ball hits the floor, it rebounds to 80% of its previous height. How high will the ball rebound after its third bounce? Round to the nearest tenth.

Answer 1

This is a geometric sequence of the form:

a(n)=ar^n, a=initial value, r=common ration, n=term number, if we relabel it for h(b) we have

h(b)=14(0.8^b)

h(3)=14(0.8^3)

h(3)≈7.2 ft (to nearest tenth of a foot)