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wrote...
2 months ago
 Calculus differential equation (not sure which type) A population r(t) of rabbits (at time t) satisfiesdr/dt = kr (1 − (r/r∗)) − αfr                                       (1)where k > 0 is a constant representing the rabbit breeding rate, r∗ > 0 is the (constant)maximum sustainable rabbit population size in the absence of predation, f > 0 is thepopulation of foxes, and α > 0 is the (constant) rate of predation of rabbits by foxes.1. Suppose that the fox population, f, is constant. Solve the differential equation(1), and determine(a) the size of the rabbit population as t → ∞;(b) the maximum predation rate α for which the rabbit population does not dieout as t → ∞;(c) the value of α which maximises αfr (the total number of rabbits caught) ast → ∞, and the corresponding rabbit population. Read 91 times 5 Replies
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wrote...
Educator
2 months ago Edited: 2 months ago, bio_man
 Hi thereI found a segment in one of my old Calculus textbooks that likely holds an explanation to your question. Please review it below, and let us know if it helps!Segment also uploaded here: https://biology-forums.com/index.php?action=downloads;sa=view;down=12400 Attached file Predator_Prey.pdf (64.23 KB) You must login or register to gain access to this attachment.
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wrote...
2 months ago
 thank you! I'll try to work through the question
wrote...
Educator
2 months ago
 You're welcome, report back if you need anything else
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wrote...
2 months ago
 Hi, I attempted to solve this but I’m not sure it’s right. I’ve attached my workings so far, could you have a look? How would I find the size of the population as t tends to infinity? Attached file(s) Thumbnail(s): You must login or register to gain access to these attachments.
wrote...
Staff Member
2 months ago
 this looks like Bernoulli's equation!substitute a very large number into t to see what happens
 - Master of Science in Biology- Bachelor of Science (Biology)- Bachelor of Education
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