Chapter 1.2, Problem 44E

To determine

To give: An example of the given situation and to sketch the original model and the shifted model.

Explanation of Solution

Given information: $d(x)=72\left|x-30\right|$ represents distance $d(inmiles)$ from the halfway point, where $x$ is the time $(indays)$ .

Calculation:

When halfway point is reached, then $d(x)=0$ .

  $\begin{array}{l}\Rightarrow 72\left|x-30\right|=0\\ \Rightarrow \left|x-30\right|=0\\ \Rightarrow x-30=0\\ \Rightarrow x=30\end{array}$

Thus, halfway point will be reached in $30$ days, so the trip will be of $60$ days.

Let the new model has a right shift of $h$ .

Then the new model is:

  $d(x)=72\left|(x-h)-30\right|=72\left|x-h-30\right|$

This means that the trip will be delayed for $h$ days from the original model.

Here, $x=0$ represents June $(1+h)$ .

For example, if $h=4$ , then $x=0$ represents June $5$ .

Graph:

  

Green colored graph represents original model and blue colored graph represents shifted model (with $h=4$ ).