MATH103 April 2013
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Question 07 (b)
Biofuel: Suppose you work at an experimental algae farm where algae is turned into biofuel. The algae grows in tanks at a rate and the steady supply of nutrients allows each tank to sustain kilograms of algae.
Suppose you harvest algae proportional to its total mass at a rate h. Modify the differential equation
accordingly. Find all steady state solutions (equilibria) for the new equation. Hint: -hM
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!
The hint in question is suggesting that you take this value away from the derivative leaving you with
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.
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As given by the hint, the new differential equation is given by
Factoring out a gives
Setting the derivative in this differential equation to 0 gives either or and isolating for gives
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MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Population dynamics, MER Tag Steady state and equilibrium, Pages using DynamicPageList parser function, Pages using DynamicPageList parser tag