Science:Math Exam Resources/Courses/MATH103/April 2016/Question 06 (a) (ii)
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Question 06 (a) (ii) 

Consider a population that is governed by the logistic differential equation with initial condition . is the population size and is time measured in years. (ii) The substitution , where is the carrying capacity found in part (i), rescales the differential equation to Write down the initial condition . 
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 

Keeping in mind that is constant, substitute . 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. From the substitution it follows that Since and we obtain 