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 9 in the function represent?

Answer 1

9 represents the initial height from which the ball was dropped

Explanation:

Bouncing of a ball can be expressed by a Geometric Progression. The function for the given scenario is:

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

The general formula for the geometric progression modelling this scenario is:

`f(n)=f_(0)(r)^(n)`

Here,

`f_(0)` represents the initial height i.e. the height from which the object was dropped.

r represents the percentage the object covers with respect to the previous bounce.

Comparing the given scenario with general equation, we can write:

`f_(0)` = 9

r = 0.7 = 70%

i.e. the ball was dropped from the height of 9 feet initially and it bounces back to 70% of its previous height every time.