The EPA has established that the air quality in a city (measured in pollution units, so high numbers mean worse air quality) depends on the number of cars driven in the city (measured in thousands)

Question

The EPA has established that the air quality in a city (measured in pollution units, so high numbers mean worse air quality) depends on the number of cars driven in the city (measured in thousands) according to the relationship I(x)= 30 + (5x -277)^(3/5).

Currently there are 75,000 cars in a city, and the number is increasing by 4,500/year. At what rate is the air quality changing?

Answer 1

I'(x) = 3(5x - 277)^-2/5·x'; f'(75) = 3(5·75 - 277)^-2/5·4.5 = 2.157 pol units/year