A ball is released at a height of 16 inches to roll inside a half-cylinder. It rollsto a height of 8 inches on the other side of the cylinder on roll 1. Each time itrolls up a side of the cylinder, the ball reaches a point that is 1/2 as high as ithad reached on the other side.This explicit formula models the height of the ball, in inches, the nth time itrolls up a side of the cylinder.an=8*(1/2) ^(n-1)How high does the ball roll on its 5th time up the cylinder's side?

Accepted Solution

Answer:[tex]\boxed{\dfrac{1}{2} \text{ in}}[/tex]Step-by-step explanation: aₙ = 8(½)ⁿ⁻¹ If n = 5  a₅ = 8(½)⁵⁻¹  a₄ = 8(½)⁴ = 8 × ¹/₁₆ = ½ in [tex]\text{On its fifth time, the ball will roll $\boxed{\mathbf{\dfrac{1}{2} in}}$ up the cylinder's side}[/tex]