Question

Rocio drops a ball from a height of 4 meters. Rocio observes that each time the ball bounces, it reaches a peak height which is 79% of the previous peak height, as shown at left. Which of the following equations correctly models the ball's peak height, h, in meters, after b bounces?

Answer 1

The exponential equation that correctly models the ball's peak height, h, in meters, after b bounces is given by:

$H(b) = 4(0.79)^b$

What is an exponential function?

A decaying exponential function is modeled by:

$A(t) = A(0)(1 - r)^t$

In which:

• A(0) is the initial value.

• r is the decay rate, as a decimal.

In this problem:

• Rocio drops a ball from a height of 4 meters, hence A(0) = 4.

• Each time the ball bounces, it reaches a peak height which is 79% of the previous peak height, hence 1 - r = 0.79.

Thus, the equation is given by:

$H(b) = 4(0.79)^b$

More can be learned about exponential equations at brainly.com/question/25537936