Question

A bouncing tennis ball starts at a height of 6 feet off the ground, and each time it bounces, it comes back up to 2/3 of the height. Which equation in inches represents the height of the ball after "x" bounces, and when will it be less than an inch off the ground?

Answer 1

The height of the bouncing tennis ball can be represented by the equation h = (2/3)^x * 6 * 12. The ball will be less than an inch off the ground after approximately 18 bounces.

Step-by-step explanation:

The height of the bouncing tennis ball can be represented by the equation h = (2/3)^x * 6 * 12, where 'h' is the height in inches and 'x' is the number of bounces. To find when the ball will be less than an inch off the ground, we can substitute 'h' with 1 in the equation and solve for 'x'.

1 = (2/3)^x * 6 * 12

Simplifying the equation, we get (2/3)^x = (1/72). To solve for 'x', we can take the logarithm of both sides of the equation.

x = log2/3(1/72)

Calculating the value of 'x', we find that the ball will be less than an inch off the ground after approximately 18 bounces.