Question

The Super Bounce brand of bouncy balls rebounds to 85% of the height from which it was dropped. Write both the explicit and recursive formulas h(n) that describes the height, h(n), of the bounce after n bounces given an initial height of 4ft.

Explicit

Recursive

Answer 1

Help me :(...

Answer 2

old question but will respond so this can be closed

remember that a recursive formula states an initial value, then states how to get to the subsequent term from the previous value.

since the initial height is 4 feet, set h(1) = 4. each subsequent value is 85% of the previous value, so simply write a formula where

(next value) = (0.85)(previous value)

and substitute the appropriate notation

Answer 3

for the explicit formula, you want to write a formula that will allow you to find the term for any term n, without having to know the previous term.

for a geometric series like this, the generic formula is

a(n) = a_1 * r^(n-1)

a_1 is already given (4), r is the ratio (0.85), leave a(n) and n alone