Question

2.  

Population Center of the US

Since the opening up of the West, the US population has moved westward. To observe this, we look at the “population center” of the US, which is the point at which the country would balance if it were a flat plate with no weight, and every person had equal weight. In 1790 the population center was east of Baltimore, Maryland. It has been moving westward ever since, and in 2000 it was in Edgar Springs, Missouri. During the second half of the 20^th century, the population center has moved about 50 miles west every 10 years.

(a)  

Let us measure position westward from Edgar Springs along the line running through Baltimore. For the years since 2000, express the approximate position of the population center as a function of time in years from 2000.

(b)  

The distance from Baltimore to Edgar Springs is a bit over 1000 miles. Could the population center have been moving at roughly the same rate for the last two centuries?

(c)  

Could the function in part (a) continue to apply for the next four centuries? Why or why not?

[Hint: You may want to look at a map. Note that distances are in air miles and are not driving distances.]

Answer 1