MATH103 April 2013
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Question 07 (d)
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.
Now suppose that you require a constant supply of algae, so you harvest it by removing algae at a constant rate . Modify the original differential equation
accordingly. Find all steady state solutions (equilibria) for this equation.
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!
Instead of we want in the differential equation.
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As mentioned in the hint above, we are looking at the modified differential equation given by
Setting the derivative to be 0, we see that
Using the quadratic formula, we see that
(Note any of the last three lines would be an acceptable answer)
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