When a ball is dropped it bounces back 90% of its hight. The ball is dropped from 2 yd. Which function models the distance the ball travels each bounce?

Question

D represents the distance traveled during the n-th bounce. (Note: 1 bounce constitutes a down and up distance.)

 

A. D=0.2(0.9)^n-1

B. D=1.8(0.9)^n-1

C. 2(0.9)^n-1

D. 3.8(0.9)^n-1

Answer 1

Let's write this out and see what the relationship is.

 

n=1: D₁ = 2 + 2(0.9)

n=2: D₂ = 2(0.9) + 2(0.9)(0.9)

n=3: D₃ = 2(0.9)(0.9) + 2(0.9)(0.9)(0.9)

 

D_n = 2(0.9)^n-1 + 2(0.9)ⁿ     now factor out 2

D_n = 2(0.9^n-1 + 0.9ⁿ)         now factor out 0.9^n-1

D_n = 2(0.9^n-1)(1 + 0.9)

D_n = 2(0.9^n-1)(1.9)

D_n = 3.8(0.9)^n-1

Answer 2

Misread the data. My error.