Question

6.2.4 practice for modeling geometric systems

Answer 1

The recursive function of a ball with a 67% rebound is a(n) = 0.67a(n-1)

The recursive function of a ball

The rebound is given as:

r = 67%

Express as decimal

r = 0.67

So, the recursive function is:

a(n) = Previous height * r

This gives

a(n) = a(n-1) * 0.67

Evaluate

a(n) = 0.67a(n-1)

Hence, the recursive function is a(n) = 0.67a(n-1)

Complete the table

Basketball

The initial height is given as:

a(1) = 54

So, we have:

a(2) = 0.67 * 54 = 36.18

a(3) = 0.67 * 36.18 = 24.24

Tennis ball

The initial height is given as:

a(1) = 58

So, we have:

a(2) = 0.67 * 58 = 38.86

a(3) = 0.67 * 38.86 = 26.04

Table-tennis ball

The initial height is given as:

a(1) = 26

So, we have:

a(2) = 0.67 * 26 = 17.42

a(3) = 0.67 * 17.42 = 11.67

Hence, the complete table is:

Bounce               n             Height

First bounce       1               Basketball: 54 inches

                                           Tennis ball: 58 inches

                                           Table tennis ball: 26 inches

Second bounce   2            Basketball: 36.18 inches

                                           Tennis ball: 38.86 inches

                                           Table tennis ball: 17.42 inches

Third bounce       3            Basketball: 24.24 inches

                                           Tennis ball: 26.04 inches

                                           Table tennis ball: 11.67 inches

Read more about geometric functions at:

brainly.com/question/5721539

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Missing part of the question

A ball is dropped such that each successive bounce is 67% of the previous bounce's height.