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?
Accepted Solution
A:
Part A: For this case we have a function of the form: [tex]y = A * (b) ^ x
[/tex] Where, A: initial height b: decrease rate x: number of bounces Substituting values we have: [tex]y = 25 * (2/5) ^ x
[/tex] Rewriting: [tex]y = 25 * (0.40) ^ x [/tex] Answer: [tex]y = 25 * (0.40) ^ x
[/tex]
Part b: See attached image
Part c: By the time the height is less than 1 inch we have: [tex]25 (0.40) ^ x \ \textless \ 1
[/tex] From here, we clear x: [tex](0.40) ^ x \ \textless \ 0.04
[/tex] Logarithm on both sides: [tex]x * log (0.40) \ \textless \ log (0.04)
[/tex] Rewriting: [tex]x * (- 1.39794) \ \textless \ (-0.39794)
[/tex] [tex]x\ \textgreater \ (-0.39794) / (-1.39794)
[/tex] [tex]x\ \textgreater \ 3.513
[/tex] Answer: x> 3.513 or x = 4