Science:Math Exam Resources/Courses/MATH103/April 2014/Question 01 (d) i
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Question 01 (d) i 

Let’s assume the size of a microbial population (in millions) at time (hours) is determined by the differential equation . Determine all steady states (or stationary states of equilibria) and circle them. (A) (B) (C) (D) (E) (F) (G) 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Recall that a steady state is one that does not evolve in time. 
Hint 2 

By the first hint, a steady state satisfies . 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Putting together the differential equation and the steady state equation , we get . For the lefthand side to be , one of its factors must be . Thus, , , or . The final answer is all of D, E and F. 