Question

The birth rate of a population is b(t) = 2000e0.023t people per year and the death rate is d(t)= 1410e0.017t people per year, find the area between these curves for 0 ≤ t ≤ 10. (Round your answer to the nearest integer.) people

Answer 1

Answer: 7118

Explanation:

Given

Birth rate is
`b(t)=2000e^(0.023t)`

Death rate is
`d(t)=1410e^(0.017t)`

Area between them is given by

`\Rightarrow A=\int _0^(10)2000e^(0.023t)-1410e^(0.017t)dt\\\Rightarrow A=\int _0^(10)2000e^(0.023t)dt-\int _0^(10)1410e^(0.017t)dt\\\Rightarrow A=22486.95652 -15368.99999\\\Rightarrow A=7117.95652`

Thus, the area between the curves is
`7117.95652\approx 7118`