Chapter 8.5, Problem 10PPS

To determine

whether the given statement is true or false.

Answer to Problem 10PPS

The statement is true

Explanation of Solution

Given:

  

Calculation:

Consider three points from the graph that shows relationship between total cost and number of rooms: $(1,110),(1,5,120)$ and $(2,140)$

In order to find constant rate of change, take any two points and use the formula for rate of change.

  $Rateofchange=\frac{changeiny}{changeinx}$

It means rate of change is change in cost with respect to change in number of rooms.

So, consider two points as: $(1,110)$ and $(1,5,120)$

Thus, constant rate of change is:

  $\begin{array}{l}Rateofchange=\frac{120-110}{1.5-1}\\ =\frac{10}{0.5}\\ =20\end{array}$

Now, take other two points $(1,5,120)$ and $(2,140)$

Thus, constant rate of change is:

  $\begin{array}{l}Rateofchange=\frac{140-120}{2-1.5}\\ =\frac{20}{0.5}\\ =40\end{array}$

Since, constant rate of change differs by taking two different points.

Therefore, the statement is true that there is not a constant rate of change.

Conclusion:

Therefore, the statement is true