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a) A colony of 1000 rabbits lives in a field that can support 5000 rabbits. After one month, the colony reaches 1050 rabbits. Use the population model with carrying capacity to predict when (in terms of the number of months from now) the colony will have 2500 rabbits. Hint: First you have to use the given data to estimate the per capita birth rate r. To do so, you may use the following logistic equation, which is the solution of the population model with carrying capacity: MP(0) P(t) = Р(0)+ (М — Р(0)e м where again P(0) is the initial population and M is the carrying capacity. After estimating r (this step is called model calibration), you can answer the question by again using EXCEL to plot of P(t) against i for 48 months at the interval of 0.5 months. Then verify your answer by using the formula above. -Mrt b) Suppose the rabbit is additionally eaten by predators at the rate of 8% per month. Add this component to the model, re-simulate the system by EXCEL and then replot the graph of rabbit population over time.

a) A colony of 1000 rabbits lives in a field that can support 5000 rabbits. After one month, the colony reaches 1050 rabbits. Use the population model with carrying capacity to predict when (in terms of the number of months from now) the colony will have 2500 rabbits. Hint: First you have to use the given data to estimate the per capita birth rate r. To do so, you may use the following logistic equation, which is the solution of the population model with carrying capacity: MP(0) P(t) = Р(0)+ (М — Р(0)e м where again P(0) is the initial population and M is the carrying capacity. After estimating r (this step is called model calibration), you can answer the question by again using EXCEL to plot of P(t) against i for 48 months at the interval of 0.5 months. Then verify your answer by using the formula above. -Mrt b) Suppose the rabbit is additionally eaten by predators at the rate of 8% per month. Add this component to the model, re-simulate the system by EXCEL and then replot the graph of rabbit population over time.

Advanced Engineering Mathematics
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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Please please answer both a and b

Thank you so much

a) A colony of 1000 rabbits lives in a field that can support 5000 rabbits. After one month, the colony reaches 1050 rabbits. Use the population model with carrying capacity to predict when (in terms of the number of months from now) the colony will have 2500 rabbits. Hint: First you have to use the given data to estimate the per capita birth rate r. To do so, you may use the following logistic equation, which is the solution of the population model with carrying capacity: MP(0) Р() + (М — Р(0)е Мит where again P(0) is the initial population and Mis the carrying capacity. After estimating r (this step is called model calibration), you can answer the question by again using EXCEL to plot of P(t) against t for 48 months at the interval of 0.5 months. Then verify your answer by using the formula above. P(t) = b) Suppose the rabbit is additionally eaten by predators at the rate of 8% per month. Add this component to the model, re-simulate the system by EXCEL and then replot the graph of rabbit population over time. Be sure to show your structural diagram (stock-flows diagram) for each problem.
Transcribed Image Text:a) A colony of 1000 rabbits lives in a field that can support 5000 rabbits. After one month, the colony reaches 1050 rabbits. Use the population model with carrying capacity to predict when (in terms of the number of months from now) the colony will have 2500 rabbits. Hint: First you have to use the given data to estimate the per capita birth rate r. To do so, you may use the following logistic equation, which is the solution of the population model with carrying capacity: MP(0) Р() + (М — Р(0)е Мит where again P(0) is the initial population and Mis the carrying capacity. After estimating r (this step is called model calibration), you can answer the question by again using EXCEL to plot of P(t) against t for 48 months at the interval of 0.5 months. Then verify your answer by using the formula above. P(t) = b) Suppose the rabbit is additionally eaten by predators at the rate of 8% per month. Add this component to the model, re-simulate the system by EXCEL and then replot the graph of rabbit population over time. Be sure to show your structural diagram (stock-flows diagram) for each problem.
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