Tuesday, October 13, 2015

Single Variable Calculus, Chapter 6, 6.1, Section 6.1, Problem 44

The equation b(t)=2200+52.3t+0.74t2 represents the birth rate of a population of people per year and the death rate d(t)=1460+28.8t people per year. Find the area between the curves for 0t10. What does this area represents?







We can use a vertical strip to evaluate the area to be


A=100[2200+52.3t+0.74t2(1460+28.8t)]dtA=100[740+23.5t+0.74t2]dtA=[740t+23.5t22+0.74t33]100A=8821.667 square units


The area bounded by the curves represents the number of people living at interval 0t10

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