Answer:
Option C is correct
4.6 feet high will the ball rebound after its third bounce
Step-by-step 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
