Question

A ball is dropped from a certain height. The function below represents the height f(n), in feet, to which the ball bounces at the nth bounce:

f(n) = 9(0.7)n

What does the number 0.7 represent?

Answer 1

As per the statement:

A ball is dropped from a certain height.

The function is given as:

`f(n)=9 \cdot(0.7)^n`

where,

f(n) represents the height in feet

n represents the number of times the ball bounces.

for n = 0

f(0) = 9

Initial height = 9

for n = 1

`f(1)=9 \cdot(0.7)^1=6.3`

For n = 2

`f(2)=9 \cdot(0.7)^2=4.41` and so on...

Since;

`(f(2))/(f(1)) = 0.7`

⇒
`f(2) = 0.7f(1)`

In general:

`f(n+1)=0.7 \cdot f(n)`

or

`f(n+1)=70\% \cdot f(n)`

therefore, 0.7 represents the ball bounces to 70% of its previous height with each bounce.

Answer 2

the 0.7 gives the next height of each bounce
For example say first bounce was 7 ft then next bounce will be t*0.7 = 4.9 ft
Then next boune will be 7*(0.7)^2 and so on.