Chapter 3.5, Problem 4ACYP

To determine

Write a function to represent this sequence

Answer to Problem 4ACYP

The required equation is $\text{L=}\text{1}\text{.5J}\text{+}\text{6}\text{.5}$

Explanation of Solution

Given:

The ordered pairs are: $(1,8),(2,9.5),(3,11),(4,12.5),$

Concept Used:

Let the number of jump is J and length in L ft.

Calculation:

Look for the pattern that can be described in an equation.

The difference between the values of jump is + 1. The difference in values for the length is L (in ft) is $9.5-8=1.5$ ft.

This suggests that the k − value is $k=\frac{1.5}{1}=1.5$ .

The suggested equation is: $\text{L=1}\text{.5}\text{J}+b$ (where b is a constant number)

Now find the value of b from the equation $\text{L=1}\text{.5}\text{J}+b$ when L = 8 ft and J = 1

  $\begin{array}{l}\text{L=1}\text{.5}\text{J}+b\\ 8=1.5·1+b[\text{L=8;}\text{J=1]}\\ 8-1.5=b\\ b=6.5\\ \text{L=}\text{1}\text{.5J}\text{+}\text{6}\text{.5}\end{array}$

The required equation is $\text{L=}\text{1}\text{.5J}\text{+}\text{6}\text{.5}$

Thus, the required equation is $\text{L=}\text{1}\text{.5J}\text{+}\text{6}\text{.5}$