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.)
A. the number of births over a 10-year period
B. the number of years it takes to increase the population by 10,000,000
C. the number of years it takes to increase the population by 10
D. the change in population over a 10-year period
E. the number of deaths over a 10-year period

Answer 1

D

Explanation:

The mathematical solution is attached in a photo. The nearest integer is 11.

Looking at the options we can eliminate B and C, as all of them refer to years. Our functions depend on years but represent changes in population, so the representation of the area MUST be in terms of population. So,B and C are wrong.

A and E refer to either death or births, but this implies only one of the functions. The area between both of them must represent both deaths and births, so answers that only mention one of them MUST be wrong.

Option D is correct. The difference between these functions represent the difference between births and deats which is population variation. It will be growth if births are greater than deaths (asit is this case).

So, option D!