Suppose you drop a ball from a height of 10 feet. after the ball hits the floor, it rebounds to a height defined by the recursiv
e formula an = 0.85an – 1. what is a1? feet what is the height the ball rebounds to after its third bounce? round your answer to three decimal places. feet
The <em>maximum</em> height of the ball after its third bounce is equal to 3.568 feet.
<h3>What is the maximum height of a ball at the third bounce?</h3>
In this question we are aware that the <em>maximum</em> height reached by the ball decreases <em>linearly</em> after each bounce. To determine that height, we must take advantage of the recursive formula described in statement:
n = 0
a₀ = 10 ft
n = 1
a₁ = 0.85 · 10 - 1
a₁ = 8.5 - 1
a₁ = 7.5 ft
n = 2
a₂ = 0.85 · 7.5 - 1
a₂ = 5.375 ft
n = 3
a₃ = 0.85 · 5.375 - 1
a₃ = 3.568 ft
The <em>maximum</em> height of the ball after its third bounce is equal to 3.568 feet.
