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.

Question

Mathematics

Smith

22 January, 12:54

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.

+3

Answers (1)

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Caiden Schaefer · 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
x (-1.39794) < (-0.39794)

x> (-0.39794) / (-1.39794)

x>3.513~4