Question

According to the Florida Agency for Workforce, the monthly average number of unemployment claims in a certain county is given by () = 22.16^2 − 238.5 + 2005, where t is the number of years after 1990. a) During what years did the number of claims decrease? b) Find the relative extrema and interpret it.

Answer 1

(a) Now from the question, we want to find during what years the number of claims decrease. Let us make the graph of the function to help us answer this

`N(t)=22.16^2-238.5t+2005`

We have

From the graph above, we can see that the function decreased at between x = 0 to x = 5.381

Hence the number of claims decreased between 1990 to 1995, that is 1990, 1991, 1992, 1993, 1994 and 1995

Note that 1990 was taken as zero

(b) The relative extrema from the graph is at 5.381, which represents 1995.

Hence the interpretation is that it is at 1995 that the minimum number of claims is approximately 1363.

Note that 1363 is approximately the y-value 1363.278