Question

using the table above, please find the rate of change and describe what it means in context.

Explanation:

Step1: Recall the rate of change formula

The rate of change formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\), where \((x_1,y_1)\) and \((x_2,y_2)\) are two points. Let \(x\) be the number of hours and \(y\) be the cost. Here, \((x_1,y_1)=(1,30)\) and \((x_2,y_2)=(4,90)\).

Step2: Substitute values into the formula

Substitute \(x_1 = 1,y_1=30,x_2 = 4,y_2 = 90\) into \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

$$m=\frac{90 - 30}{4 - 1}=\frac{60}{3}$$

Step3: Calculate the rate of change

\(\frac{60}{3}=20\)

In the context of the problem, the \(x\)-values represent hours and the \(y\)-values represent cost. The rate of change of \(20\) means that for each additional hour, the cost increases by \(20\) dollars.

Answer:

The rate of change is \(20\). It means that the cost increases by \(20\) dollars per hour.