If the birth rate of a population is b(t) = 3600e0.034t people per year and the death rate is d(t) = 1530e0.014t people per year, then the increase in population over a 5-year period is equal to the area between these curves for 0 ≤ t ≤ 5. Thus, the increase in population during that period is equal to fodt =
If the birth rate of a population is b(t) = 3600e0.034t people per year and the death rate is d(t) = 1530e0.014t people per year, then the increase in population over a 5-year period is equal to the area between these curves for 0 ≤ t ≤ 5. Thus, the increase in population during that period is equal to fodt =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Book Problem 31
If the birth rate of a population is \( b(t) = 3600e^{0.034t} \) people per year and the death rate is \( d(t) = 1530e^{0.014t} \) people per year, then the increase in population over a 5-year period is equal to the area between these curves for \( 0 \leq t \leq 5 \).
Thus, the increase in population during that period is equal to \( \int_{0}^{5} \left( b(t) - d(t) \right) dt = \int_{0}^{5} \left( 3600e^{0.034t} - 1530e^{0.014t} \right) dt \).
### Detailed Explanation:
To find the increase in population over a given period, you need to calculate the area between the birth rate curve \( b(t) \) and the death rate curve \( d(t) \). This is achieved by integrating the difference of these two functions over the specified interval \( [0, 5] \).
\[ \int_{0}^{5} \left( 3600e^{0.034t} - 1530e^{0.014t} \right) dt \]
This integral represents the net increase in population by taking into account the births and deaths over the 5-year period. By solving this integral, you will determine the total change in population.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe8fabc15-e5db-480c-94d9-e42b67b656a8%2Fd41add3e-1349-4f39-8f44-2dbbd12bc9e9%2Fc3dif6p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Book Problem 31
If the birth rate of a population is \( b(t) = 3600e^{0.034t} \) people per year and the death rate is \( d(t) = 1530e^{0.014t} \) people per year, then the increase in population over a 5-year period is equal to the area between these curves for \( 0 \leq t \leq 5 \).
Thus, the increase in population during that period is equal to \( \int_{0}^{5} \left( b(t) - d(t) \right) dt = \int_{0}^{5} \left( 3600e^{0.034t} - 1530e^{0.014t} \right) dt \).
### Detailed Explanation:
To find the increase in population over a given period, you need to calculate the area between the birth rate curve \( b(t) \) and the death rate curve \( d(t) \). This is achieved by integrating the difference of these two functions over the specified interval \( [0, 5] \).
\[ \int_{0}^{5} \left( 3600e^{0.034t} - 1530e^{0.014t} \right) dt \]
This integral represents the net increase in population by taking into account the births and deaths over the 5-year period. By solving this integral, you will determine the total change in population.
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