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

Consider a population that is governed by the logistic differential equation with initial condition . is the population size and is time measured in years. (v) How long will it take for the population to reach 50% of the carrying capacity? 
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Hint 

Use the results in part (ii) and part (iv). 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. From part (ii) and (iv), we have that if and then Let be the time at which the population reaches 50% of the carrying capacity. Then, at the time we know that and therefore Thus, we solve the following equation to find the time: So, we have and finally 
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Nobody voted on this yet Hard Easy 