The population density r miles from the center of a city is $D ( r ) = k e ^ { - 0.5 r ^ { 2 } }$ people per square mile. If 300,000 people live within 5 miles from the center of the city, then k is 15,000.

Question

Quizplus · Accepted Answer

To find k, integrate the population density function over the area within 5 miles and set it equal to 300,000. Solving this integral will show that k is not 15,000.

The Population Density R Miles from the Center of a City