Question

If a ball is dropped from a height of 18 ft the function f(x)=18 (0.75)^xgives the height in feet of each bounce, where x is the bounce number. What will the height of the 7th bounds to the nearest tenth of a foot

Answer 1

f ( 7 ) = 2.4 ft

Explanation:

Solution:-

- This is modeled using a geometric sequence function with initial height from which ball is dropped hi = 18 feet, and a decrease in height by 25% after each successive bounce :

f ( x ) = 18 (0.75)^x

Where, x e [ 0 , ∞ ) : The number of bounces.

f (x) : The maximum height after xth bounce.

- The maximum height reached by the ball after its 7th bounce. So, x = 7:

f ( 7 ) = 18 (0.75)^7

f ( 7 ) = 2.4027 ft

- To the nearest tenth:

f ( 7 ) = 2.4 ft