Question

dn n(0)=1 = rn. dt Main activity (2.5 marks) (a) If we modify Eq. *) to model a growing population with an additional con- stant rate of immigration, a, we get dn n(0) = 1. = rn a, dt Solve this using the integrating factor method (b) Another population growth model is the logistic equation dn - гn(1 — п). dt Solve this, with the initial condition n(0) = 1/10 (c) Adding immigration, a, the logistic equation becomes dn — гn(1 — п) + а. dt i. Draw the phase diagram for this equation, assuming r > 0 and a > 0 ii. For this equation, there are two values of n for which dn 0. dt Suppose we used this equation to model a population of mice. Which steady state would we use and why?

Answer 1

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