Help please!!! A circular city has a radius of r miles and an average population density of p ( ro) people/mi^2. In 2012 the population density was 15,000 plp/mi^2, the radius was 3 miles and growing at .1/mile/year. If the density was decreasing at 1000 people.mi^2/yr then use the chain-rule to determine at what rate the total population of the city was changing

Question

Help please!!! A  circular city has a radius of r miles and an average population density of p ( ro) people/mi^2. In 2012 the population density was 15,000 plp/mi^2, the radius was 3 miles and growing at .1/mile/year. If the density was decreasing at 1000 people.mi^2/yr then use the chain-rule to determine at what rate the total population of the city was changing

miracrown · Answer

The population= the area * the density.
P = A x P

miracrown · Answer

We are considering a circular region, so the area is pi*r^2, where r is the radius.

miracrown · Answer

$$P = A \times P \space = \pi r ^{2} $$

miracrown · Answer

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