The city of Compass Station is in the shape of a circle of radius 6 miles, as shown in the graph below, where the grid is shown in miles along each axis.



The population density is $\displaystyle {4500}{\frac{{\text{people}}}{{\text{mile}^{{2}}}}}$ at the center of town, decreasing linearly to $\displaystyle {3300}{\frac{{\text{people}}}{{\text{mile}^{{2}}}}}$ at the edge of town.

Let $\displaystyle \delta{\left({r}\right)}$ represent the population density of points in the city that are $\displaystyle {r}$ miles from the center.Write a formula for the population density.

$\displaystyle \delta{\left({r}\right)}=$Preview Question 6 Part 1 of 7   $\displaystyle {\frac{{\text{people}}}{{\text{mile}^{{2}}}}}$