Question

The birth rate of a population is b(t) = 2500 e0.021t people per year and the death rate is d(t)= 1470 e0.019t people per year, find the area between these curves for 0 ≤ t ≤ 10. (Round to the nearest integer.)What does this area represent? (Attention! You are allowed only two submissions for this answer.)the number of births over a 10-year periodthe number of years it takes to increase the population by 10,000,000the number of years it takes to increase the population by 10the change in population over a 10-year periodthe number of deaths over a 10-year period

Answer 1

110,323.7505 or 110,324

Explanation:

We need to take the integral of b(t) - d(t) over the interval of [0, 10]. This will tell us the average population over a 10 year period.

We are counting all the birth (additions to the population) and counting the deaths (subtractions to the population), so overall population is calculated by:

Population = birth rate - death rate

We take the anti derivatives of b(t) and d(t), see all work on the attached photo