There are ten problems totaling 10 points. Show all your work! 1. Wildlife manag

Question

There are ten problems totaling 10 points. Show all your work! 1. Wildlife management A certain whitetail deer population in a closed eco-system grows exponentially at an intrinsic growth rate of 0.4 per year. Meanwhile, regulated hunting harvests h deer per year from the population. Therefore, the deer population is described by the differential equation y'-04y-k. Suppose there are initially 9000 deer. (a) Given a year culling quota of h 2500. Find the deer population y(). (b) How long does it take for the colony to double in size? (c) [Zero-growth scenario] Find the value of culling quota h that will be necessary to maintain the deer population at its present, constant, level.

Explanation / Answer

Answer

Given

y' = 0.4y - h

then

rate = dy'/dt

dr/dt = d (0.4y - h)/dt

dr/dt = 0.4

So, growth rate of a deer is independent of hunting.

Initially, total deer = 9000

No of deer grow per day = 9000 X 0.4 = 3600

No. of deer after one year = 9000 + 3600 = 12600

Hunting quota = 2500

Total deer population after one year = 12600-2500 = 10100 deer.

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