The height, f (x), of a bouncing ball after x bounces is represented by f (x) = 80 (0.5) ^x. How many times higher is the first bounce than the fourth bounce?

A.

2

B.

4

C.

6

D.

8

D) 8

Step-by-step explanation:

Given function for height = f (x) = 80 (0.5) ^x

It shows that the height of ball after any bounce can be calculated by putting bounce number in place of x in this equation.

so, height after first bounce f (1) is calculated by placing 1 in place of x

f (1) = 80 (0.5) ^1

f (1) = 80 (0.5)

f (1) = 40

Similarly, the height after 4th bounce f (4)

f (4) = 80 (0.5) ^4

f (4) = 80 (0.0625)

f (4) = 5

Therefore, the height of 1st bounce is 40/5 = 8 times higher than the fourth bounce. So, option D is correct.