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Program Description: Purpose of problem is to calculate the number of months takes for
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Explanation of Solution
Given information:
The logistic equation is
Here,
Initial population is 120 with rate of 8 births per month and 6 deaths per month.
Take initial time as 0.
Explanation:
The solution of the logistic differential equation is shown below.
Here,
Obtain the maximum capacity of the system
Obtain the value of
Now, substitute the known values
To obtain the time at which population reaches to 95% of maximum population, substitute
Further, solve the equation as follows:
Conclusion:
Therefore, the number of months takes for
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Chapter 2 Solutions
EBK DIFFERENTIAL EQUATIONS
- Suppose that a particular plot of land can sustain 500 deer and that the population of this particular species of deer can be modeled according to the logistic model as dPdt=0.2(1P500)P. Each year, a proportion of the herd deer is sold to petting zoos. a. Find the function that gives the equilibrium population for various proportions. b. Determine the maximum number of deer that should be sold to petting zoos each year. Hint: Find the maximum sustainable harvestarrow_forwardTo the nearest whole number, what is the initial value of a population modeled by the logistic equation P(t)=1751+6.995e0.68t ? What is the carrying capacity?arrow_forwardWhat does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?arrow_forward
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