Mathematics Help

Question

The birth rate of a population is b(t) = 2400e^0.021t people per year and the death rate is d(t)= 1490e^0.015t

 people per year, find the area between these curves for 0 ≤ t ≤ 10. (Round your answer to the nearest integer.)

Answer 1

This question can be evaluated via a simple integral. First, let's get a rough graph of what we are trying to find.

Essentially, we will be subtracting the area under the red curve(b(t)) from the area under the blue curve(d(t)) in order to get that middle region. Thus, our integral become a definite integral from 0 to 10 of 2400e^0.021t-1400e^0.015t with respect to t.

Solving for this integral, we get 10630.52921738025 --> 10631.