Science:Math Exam Resources/Courses/MATH103/April 2016/Question 06 (a) (v)/Solution 1

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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