Question

The birth rate of a population is b(t) = 2300e0.021t people per year and the death rate is d(t)= 1450e0.018t people per year, find the area between these curves for 0 ≤ t ≤ 10. (Round your answer to the nearest integer.) people What does this area represent? This area represent the number of children through high school over a 10-year period. This area represents the increase in population over a 10-year period. This area represents the decrease in population over a 10-year period. This area represents the number of deaths over a 10-year period. This area represents the number of births over a 10-year period.

Answer 1

Answer:

38,674.This area represents the increase in population over a 10-year period.

Step-by-step explanation:

When graphed over the interval 0 ≤ t ≤ 10, the birth rate is more than the death rate. This means the area between the two curves is the amount of births subtract the amount of deaths. This results in an area which means the increase of the population.

The birth rate is graphed in green and the death rate is graphed in blue.

To find the area, take the integral of the difference of the functions:

$\int\limits^{10}_0 {2300e^{0.021t} - 1450e^{0.018t} } \, dt \\\\\frac{2300e^{0.021t}}{0.021} - \frac{1450e^{0.018t}}{0.018} \\\\(\frac{2300e^{0.21}}{0.021} -\frac{1450e^{0.18}}{0.018} ) - (\frac{2300}{0.021}- \frac{1450}{0.018} ) \\\\135117.12 - 96442.51 \\\\38,674$