what is the answer to C? Please also include a graph for this entire question.

Topic 1: 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 20th 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. Because the center moved 50 miles in the 10 years you would do (50/10=5) to get the function f(t)=5t. This calculates the amount of miles the center moved from Edgar Springs since 2000. The 5 in the equation represents the 5 miles it moves every year and the t is the (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? The problem states since moving from the West the US population has been moving westward. The center was considered to be east of Baltimore in 1790, and ever since it has continued to keep moving west. The population center is now in Edgar Springs in the year 2000, and continues to move about 50 miles every 10 years. So if we see the change in 210 years (2000-1790) the populations has moved west by about 1050 miles (210 years/10=21) (21 years * 50 miles=1050 miles). Seeing the movement of the population center shifting west, comparing the 2 major events given in the problem, it looks as if both major events have had a consistency in movement of miles. So I believe that the population center could have been moving at roughly the same rate for the last 2 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.]