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

Let’s assume the size of a microbial population (in millions) at time (hours) is determined by the differential equation . True or false: if is in the interval , then the population will stay inside this interval. 
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 

Use the result of part i) 
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 

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Please rate my easiness! It's quick and helps everyone guide their studies. If is in , then in order for to lie outside of , by continuity and the Intermediate Value Theorem, there must a time such that or . But since and are steady states, if this occurs then will be (respectively, ) for all . The statement is true. 