Question

A new softball dropped onto a hard surface from a height of 25 inches rebounds to about 2/5 the height on each successive bounce.

a. Write a function representing the rebound height for each bounce.
b. Graph the function.
c. After how many bounces would a new softball rebound less than 1 inch?

Answer 1

Part A:
For this case we have a function of the form:

`y = A * (b) ^ x`
Where,
A: initial height
b: decrease rate
x: number of bounces
Substituting values we have:

`y = 25 * (2/5) ^ x`
Rewriting:

`y = 25 * (0.40) ^ x`
Answer:

`y = 25 * (0.40) ^ x`

Part b:
See attached image

Part c:
By the time the height is less than 1 inch we have:

`25 (0.40) ^ x \ \textless \ 1`
From here, we clear x:

`(0.40) ^ x \ \textless \ 0.04`
Logarithm on both sides:

`x * log (0.40) \ \textless \ log (0.04)`
Rewriting:

`x * (- 1.39794) \ \textless \ (-0.39794)`

`x\ \textgreater \ (-0.39794) / (-1.39794)`

`x\ \textgreater \ 3.513`
Answer:
x> 3.513 or x = 4