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

MATH103 April 2014

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Question 01 (d) ii
Let’s assume the size of a microbial population $x(t)$ (in millions) at time $t$ (hours) is determined by the differential equation ${\frac {dx}{dt}}=x(1-x)(x-1/2)$. True or false: if the initial population is $x(0)=0$, then the population $x(t)$ will converge to the stationary state $x=1/2$ as $t\to \infty$.

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).

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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. If the initial population is $0$, then it will be $0$ forever, as 0 is a steady state. The statement is false.

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