Question

The birth rate of a population is b(t) = 2300e0.024t people per year and the death rate is d(t)= 1450e0.019t people per year, find the area between these curves for 0 ≤ t ≤ 10. (Round your answer to the nearest integer.)

Answer 1

Answer:

Area = 10025.66 square units

Step-by-step explanation:

We are given the following in the question:

The birth rate of a population:

$b(t) = 2300e^{0.024t}$

The death rate of a population:

$d(t)= 1450e^{0.019t}$

The area between the curve for 0 ≤ t ≤ 10, is given by:

$\displaystyle\int_0^{10}b(t) - d(t)~ dt\\\\\displaystyle\int_0^{10} 2300e^{0.024t}-1450e^{0.019t}~dt\\\\= \Bigg[\frac{2300e^{0.024t}}{0.024}\Bigg]_0^{10}-\Bigg[\frac{1450e^{0.019t}}{0.019}\Bigg]_0^{10}\\\\= \Bigg[\frac{2300e^{0.24}}{0.024}-\frac{1450e^{0.19}}{0.019}\Bigg]-\Bigg[\frac{2300}{0.024}-\frac{1450}{0.019}\Bigg]\\\\= 29543.2058565 - 19517.5438596 \approx 10025.6$