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?

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