Question

 A rubber ball is dropped onto a hard surface from a height of 8 feet, and it bounces up and down. At each bounce it rises to 90% of the height from which it fell.

a.  Find a formula for 

h(n) , the height in inches reached by the ball on bounce  n .
h(n)=?
b.  How high will the ball bounce on the  14th  bounce? (in inches)
c.  How many bounces before the ball rises no higher than an inch? 

Answer 1

a. 8 feet * 0.9 = distance after first bounce
h(n) = 8 * 0.9^n

b. 8 * 0.9^14 = 1.83 feet to 2 d.p.
1.83 * 12 = 21.96 inches