In this problem, we have a table that shows living wages in Rochester. This study was made over a 5 year period. For a function of [tex]f[/tex], the average rate of change can be found as follows:
[tex] ARC=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}} [/tex]
So, let's find the two ARC.
1. Average Rate of Change in the number of living wage jobs from 1997 to 1999:
In this item, we have that:
[tex] x_{1}=1997 \\ x_{2}=1999 \\ \\ f(x_{1})=635 \\ f(x_{2})=745 [/tex]
Therefore, the ARC is:
[tex] ARC=\frac{745-635}{1999-1997} \\ \\ \therefore \boxed{ARC=55} [/tex]
So, from 1997 to 1999 the number of living wage jobs increases at a rate of 55 jobs per year
2. Average Rate of Change in the number of living wage jobs from 1999 to 2001:
In this item, we have that:
[tex] x_{1}=1999 \\ x_{2}=2001 \\ \\ f(x_{1})=745 \\ f(x_{2})=800 [/tex]
Therefore, the ARC is:
[tex] ARC=\frac{800-745}{2001-1999} \\ \\ \therefore \boxed{ARC=27.5} [/tex]
So, from 1999 to 2001 the number of living wage jobs increases at a rate of 27.5 jobs per year
