The US Census Bureau regularly tries to estimate the number of people who live along various highways. One important highway is I-95, which runs from Miami up the coast through Maine.

In 2010, the Census Bureau measured the population density within 5 miles of I-95 at regularly-spaced distances, starting at Miami and going 100 miles north. They produced the following model:

P(d) = -.044d³+6.56d²-341.3d+10151

Measured in people per square mile at a distance d from Miami.

How many people live within 5 miles of I-95 along this 100-mile stretch of the highway?

Preparation:

1. Draw a picture of the 5-mile-wide stretch of I-95, labeling all dimensions, and representing the variable population density.
2. Is there less, the same, or more people living in the first 50 miles compared to the last 50 miles? Explain.
3. Explain why we cannot just multiply a population density by the area of the shape you drew in question 1.