Chapter 8.6, Problem 30SR

To determine

To compare: the rate of change.

Answer to Problem 30SR

The rate of change of pears is $\$1.2perweight$

The rate of change of oranges is $\$1.1perweight$

Explanation of Solution

Given: Consider the table showing the cost of pears and oranges.

  

Calculation:

The objective is to compare the rate of change.

For pears, consider two pairs of points, say $(2,2.40)and(5,6)$

Now,

  $\begin{array}{l}Rateofchnage=\frac{Chnagein\cos t(\$)}{changeinweight(lb)}\\ =\frac{6-2.40}{5-2}\\ =1.2\$/lb\end{array}$

Therefore the rate of change of pears is $\$1.2perweight$

For oranges, consider two pairs of points, say $(2,2.20)and(5,5.5)$

Now,

  $\begin{array}{l}Rateofchnage=\frac{Chnagein\cos t(\$)}{changeinweight(lb)}\\ =\frac{5.5-2.20}{5-2}\\ =1.1\$/lb\end{array}$

Therefore the rate of change of oranges is $\$1.1perweight$

Conclusion:

The rate of change of pears is $\$1.2perweight$

The rate of change of oranges is $\$1.1perweight$