Question

Use the following graph to answer the next three questions. find the rate of change in the number of new job openings for each month interval below. round your answers to the nearest tenth.

Answer 1

Given the rate of change formula

`\begin{gathered} At\text{ interval}\rightarrow[a,b] \\ Rate\text{ of change is} \\ m=(f(b)-f(a))/(b-a) \end{gathered}`

Since we are calculating the rate of change for each month, the interval difference is 1

Thus

From January(a) and July(b)

`\begin{gathered} m_=(f(b)-f(a))/(b-a) \\ f(b)=110 \\ f(a)=10 \\ b=7 \\ a=1 \end{gathered}`
`\begin{gathered} m=(110-10)/(7-1)=(100)/(6) \\ m=16.667\approx16.7\text{ jobs per month} \end{gathered}`

Hence, the rate of change in the number of new job openings for each month from January to July is 16.7 jobs per month