### Home > GB8I > Chapter 8 Unit 9 > Lesson INT1: 8.1.4 > Problem8-59

8-59.

Jeffe and Tomas collected the following data for a bouncing basketball. What is their rebound ratio as a percent? Write a model for their data and then sketch a graph of the situation.

 Bounce number ($x$) $1$ $2$ $3$ $4$ Height, cm ($y$) $80$ $64$ $51$ $41$

Look at the ratios of the successive $y$-values.

$\frac{64}{80}=0.8 \ \ \ \ \frac{51}{64}\approx 0.8$

Use the general form of an exponential equation: $y = a \cdot b^{x}$. The parameter, $b$, is the constant ratio, $0.8$.
To find the $a$-value, find the $0^{th}$ term.

To find the $0^{th}$ term, divide the first term, $80$, by $0.8$