A rubber ball is dropped onto a hard surface from a height of 9 feet, and it bounces up and down. At each bounce it rises to 80% 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 10 bounce?

c. How many bounces before the ball rises no higher than an inch?

There are 12 inches in a foot, so 9ft = 108in. Also, 80% = 0.8. Therefore the formula is: h (n) = 108 * 0.8^n. To find the bounce height after 10 bounces, substitute n=10 into the equation: h (n) = 108 * 0.8^10 = 11.60in (2. d. p.). Finally to find how many bounces happen before the height is less than one inch, substitute h (n) = 1, then rearrage with logarithms to solve for the power, x: 108 * 0.8^x = 1; 0.8^x = 1/108; Ln (0.8^x) = ln (1/108); xln (0.8) = ln (1/108); x = ln (1/108) / ln (0.8) = - 4.682 / - 0.223 = 21 bounces