A population of shrimp in lake has exceeded the carrying capacity of lake. If the population growth is represented by the given phase line,

It is observed that growth of population is logistic with very high growth rate. Which of the following solution curve best represent the population of shrimp over time?

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Calculus 2

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Analyze phase planes

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24 Jul 2020

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Related questions

The logistic function in form of differential equation is given by,

where, P is population growth as function of time, ‘r’ is the growth rate and K is the carrying capacity.

If the carrying capacity is the also function of time K(t) and changing with time given as ,

How the population growth will follow the varying carrying capacity?

Environment A conservation department releases

1200 brook trout into a lake. It is estimated that the carrying capacity of the lake for the species is 20,400. After the first year, there are 2000 brook trout in the lake.

(a) Write a logistic equation that models the number of brook trout in the lake.

(b) Find the number of brook trout in the lake after 8 years.

(d) Write a logistic differential equation that models the growth rate of the brook trout population. Then repeat part (b) using Euler’s method with a step size of . Compare the approximation with the exact answer.

(e) At what time is the brook trout population growing most rapidly? Explain.

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