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.

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:

[tex]\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[/tex]

psm22415 psm22415 · Answer 2 · 2022-02-16T08:08:52+01:00

The area between these curves for 0 ≤ t ≤ 10 is 38674.

The area represents the increase in population over a 10-year period

Given

The birth rate of a population is [tex]\rm b(t) = 2300e^{0.021t }[/tex] people per year.

And the death rate is [tex]\rm d(t)= 1450e^{0.018t}[/tex] people per year.

What is integration?

Integration is the reverse of differentiation.

When graphed over the interval 0 ≤ t ≤ 10, the birth rate is more than the death rate.

The area given the difference between the number of births and the number of deaths, which gives the net number of persons added to the population, or the net population increase over the 10 year period.

Therefore,

The area between these curves for 0 ≤ t ≤ 10 is given by subtracting birth rate and death rate.

[tex]\rm Area \ between \ curves = \int\limits^{10}_0 {(Birth \ rate - Death \ rate)} \, dt\\\\\rm Area \ between \ curves = \int\limits^{10}_0(\rm 2300e^{0.021t }-\rm 1450e^{0.018t)}dt\\\\Area \ between \ curves = \left[ \dfrac{ 2300e^{0.021t }}{0.021}-\dfrac{1450e^{0.018t}}{0.0108} \right ]^{10}_0\\\\Area \ between \ curves =1351117.12-96442.51\\\\Area \ between \ curves =38,674[/tex]

Hence, the area between these curves for 0 ≤ t ≤ 10 is 38674.

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