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.

Recursive formula

Explicit formula

Step-by-step explanation:

An explicit formula allows you to find the value of any term in the sequence. A recursive formula allows you to find the value of the nth term if you know the value of the (n-1)th term in the sequence.

Recursive formula

Given the initial height (), the next height () is 85% of it, the following height is 85% of the new height, and so on. Mathematically:

Where () is the nth height, given the previous one ()

Explicit formula

initial height: 4 ft

n: number of bounces

h(n): height after n bounces

n    h(n)

1    4*0.85 = 3.4 ft

2    3.4*0.85 = 2.89 ft

3    2.89*0.85 = 2.4565 ft

...  ...

n    4*0.85^n

complete the steps to find the area of the trapezoid.

area of rectangle = 256   square units

area of triangle 1 = 24  square units

area of triangle 2 = 16  square units

area of triangle 3 =   96 square units

area of trapezoid = 120  square units

step-by-step explanation: