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?

f(x) = 25(0.4)x; 6 bounces.
f(x) = 0.4(25)x; 6 bounces.
f(x) = 25(0.4)x; 4 bounces.
f(x) = 0.4(25)x; 4 bounces.

Answer 1

let f(x) be the height reached after x=0,1,2,3....
f(0) be the original height f(0)=25 in
then:
f(x)=f(0)(0.40)^x
since f(0)=25
f(x)=25(0.40)^x

the number of bounces that it will take for rebound to be less than 1 will be:
25(0.4)^x<1
this can be written as:
0.4^x<0.04
introducing natural logs we get:
xln0.4<ln0.04
x(-1.39794)<(-0.39794)
x>(-0.39794)/(-1.39794)
x>3.513~4