Q40. - Algebra 2

Question

For Exercises 40-42 use the following information.

Mr. and Mrs. Wellman are taking their daughter to college. The table shows their distance from after various amounts of time.

40. Find the average rate of change of their distance from home between 1 and 3 hours after leaving home.

Step-by-Step Solution

Answer

The average rate of change of their distance from home between 1 and 3 hours after leaving home is $55.$

Step 1- Given information

The table of the given data,

Step 2- Formula used

The slope formula (rate of change) m of a line is:

$m=\frac{y_2-y_1}{x_2-x_1}$

Where, m is slope of the line which is passes through the points $(x_1,y_1),(x_2,y_2)\text{ and }{x}_1\ne x_2.$

Step 3- To find the Rate of change

Here, $(x_1,y_1)=(1,55){\text{ and (x}}_2,y_2)=(3,165)$

So,  $m=\frac{y_2-y_1}{x_2-x_1}$

$\begin{array}{l}\Rightarrow m=\frac{165-55}{3-1}\\ \Rightarrow m=\frac{110}{2}\\ \Rightarrow m=55\end{array}$

Hence, the average rate of change of their distance from home between 1 and 3 hours after leaving home is $55.$