Question

Δt gets smaller). Question 3: (4 marks) In deriving the logistic equation for population growth, we assumed the growth rate was proportional to the amount of excess resources, FA pFR where FA is the amount of available resources, p the population, and FR the amount of resources required per individual. Due to seasonal effects, FA may not be a constant (a) Derive a logistic-type equation assuming the amount of resources available are FA(1 + e sin(wt)), where 0 < e < 1 is a small parameter. This could represent, for example, more or less tood being available at certain times of the year. Your equation should be dt = ap(H, (1 + esin (at))-pFr). (b) Find a two-term approximation of the solution to this equation, if the initial population size is p(0) = C. Hint: First let k = aFa and C = FA/FR to simplify the notation. (c) What happens if w is very large, or if it is very small?
question 3

Answer 1

dP → population growth 5 Yous dt 1O) dt- = ap ( FA-PER) d P dlt

dt pt df olt P(tl Nou. Soluti an Com be witen in integycing R. l Constant

Simuut C E) Sinut
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