Question

Suppose you drop a tennis ball from a height of 9 feet. After the ball hits the floor, it rebounds to 80% of its previous height. How high will the ball rebound after its third bounce? Round to the nearest tenth.

A) 5.8 feet
B) 1 feet
C) 4.6 feet
D) 7.2 feet

Answer 1

9(.80) = 7.2(.80) =  5.76(.80) = 4.608. round it and it is 4.6 feet

Answer 2

Option C is correct

4.6 feet high will the ball rebound after its third bounce

Explanation:

Using the Explicit sequence formula is given by:

`f(n)= ar^n`

where,

a is the initial value

r is the common ratio.

As per the statement:

Suppose you drop a tennis ball from a height of 9 feet.

⇒a = 9 feet

It is also given that:

After the ball hits the floor, it rebounds to 80% of its previous height.

⇒
`r = 80\% = 0.80`

then;

An explicit sequence is,

`f(n) = 9 \cdot (0.80)^n` ....[1] where, n is the number of times bounce ball.

We have to find how high will the ball rebound after its third bounce

Substitute n = 3 in [1] we have;

`f(3) = 9 \cdot (0.80)^3 = 9 \cdot 0.512 = 4.608` ft

Therefore, 4.6 feet high will the ball rebound after its third bounce