Question

A tennis ball is dropped from an initial height of 30 feet. It bounces 5 times, with each bounce height being about 2/3 of the height of the previous bounce.

Answer 1

Answer:

Step-by-step explanation:

I'm thinking you want to know the height of the ball on that 5th bounce, right? This is of the form

$y=a(b)^x$

where a is the initial height and b is the decay factor.  If the ball comes up to 2/3 of its height from the previous bounce, then b = 2/3 and our equation is

$y=30(\frac{2}{3})^x$

If you want to know the height y of the 5th bounce x, sub in a 5 for x and solve for y:

$y=30(\frac{2}{3})^5$ and get that

y = 320/81 or as a decimal, 3.9506 feet