Chapter 5.1, Problem 8PPE

To determine

To determine if the rate of change in cost constant. Explain what it represents.

Answer to Problem 8PPE

The rate of change in time is not constant with the rate of change of distance.

Explanation of Solution

Given Information:

The table is given with the following data.

Solution:

Turtle Walking
Time (in min)	Distance (m)
$1$	$6$
$2$	$12$
$3$	$15$
$4$	$21$

Consider the points $A\left(x_1,y_1\right)=\left(1,6\right)$

  $B\left(x_2,y_2\right)=\left(2,12\right)$

  $C\left(x_3,y_3\right)=\left(3,15\right)$

  $D\left(x_4,y_4\right)=\left(4,21\right)$

To find the rate of change find the slope as following.

Formula used: The slope between the points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is calculated as follows.

  $m=\frac{y_2-y_1}{x_2-x_1}$

Calculate the slope between the points $A\left(x_1,y_1\right)=\left(1,6\right)$ and $B\left(x_2,y_2\right)=\left(2,12\right)$

  $\begin{array}{c}{m}_1=\frac{12-6}{2-1}\\ =\frac{6}{1}\\ =6\end{array}$

The slope between the points $A\left(x_1,y_1\right)=\left(1,6\right)$ and $B\left(x_2,y_2\right)=\left(2,12\right)$ is $6$ .

Calculate the slope between the points $B\left(x_2,y_2\right)=\left(2,12\right)$ and $C\left(x_3,y_3\right)=\left(3,15\right)$

  $\begin{array}{c}{m}_2=\frac{15-12}{3-2}\\ =\frac{3}{1}\\ =3\end{array}$

The slope between the points $B\left(x_2,y_2\right)=\left(2,12\right)$ and $C\left(x_3,y_3\right)=\left(3,15\right)$ is $3$

Calculate the slope between the points $C\left(x_3,y_3\right)=\left(3,15\right)$ and $D\left(x_4,y_4\right)=\left(4,21\right)$

  $\begin{array}{c}{m}_3=\frac{21-15}{4-3}\\ =\frac{6}{1}\\ =6\end{array}$

The slope between the points $C\left(x_3,y_3\right)=\left(3,15\right)$ and $D\left(x_4,y_4\right)=\left(4,21\right)$ is $6$

The slope is not same in for all the three set of points. The rate of change in time is not constant with the rate of change of distance.