Question

A ball is released at a height of 16 inches to roll inside a half-cylinder. It rolls

to a height of 8 inches on the other side of the cylinder on roll 1. Each time it
rolls up a side of the cylinder, the ball reaches a point that is 1/2 as high as it
had reached on the other side.
This explicit formula models the height of the ball, in inches, the nth time it
rolls 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?

Answer 1

Answer: 1/2 inch

Step-by-step explanation: Letter d

Answer 2

`\boxed{(1)/(2) \text{ in}}`

Explanation:

aₙ = 8(½)ⁿ⁻¹

If n = 5

a₅ = 8(½)⁵⁻¹

a₄ = 8(½)⁴ = 8 × ¹/₁₆ = ½ in

`\text{On its fifth time, the ball will roll $\boxed{\mathbf{(1)/(2) in}}$ up the cylinder's side}`