Science:Math Exam Resources/Courses/MATH103/April 2013/Question 07 (d)
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q2 (a) • Q2 (b) • Q2 (c) • Q2 (d) • Q3 (a) • Q3 (b) i • Q3 (b) ii • Q4 (a) • Q4 (b) • Q5 (a) • Q5 (b) • Q6 (a) • Q6 (b) • Q6 (c) • Q7 (a) • Q7 (b) • Q7 (c) • Q7 (d) • Q7 (e) • Q8 (a) • Q8 (b) • Q8 (c) • Q9 • Q10 •
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! 
Hint 

Instead of we want in the differential equation. 
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.

Solution 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. 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) 