5.11.6 Practice

For questions 1 – 4, use the following:

Function $h$ describes the height of a ball, in inches, after $n$  by the equation $h(n)=120\cdot <!--\; \cdot \; -->(\frac{4}{5}{)}^n$.

1. What is $h(3)$? Round to the nearest integer. Think about what it represents in this situation.

2. Could $h(n)$ be 150?

3. Which ball loses its height more quickly, this ball, modeled by $h(n)=120\cdot <!--\; \cdot \; -->(\frac{4}{5}{)}^n$, or a tennis ball whose height in inches after $n$ bounces is modeled by the function $f$ where $f(n)=50\cdot <!--\; \cdot \; -->(\frac{5}{9}{)}^n$ ?

4. How many bounces would it take before the ball, modeled by $h(n)$, bounces less than 12 inches from the surface?

5. After a second bounce, a ball reached a height of 70 cm. The rebound factor for the ball was 0.8. From approximately what height, in cm, was the ball dropped?

6. Using the table below, find the height, in cm, at which the ball was dropped.