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
