009A Sample Midterm 1, Problem 2 Detailed Solution

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Suppose the size of a population at time    is given by

(a) Determine the size of the population as    We call this the limiting population size.

(b) Show that at time    the size of the population is half its limiting size.

Background Information:  
Recall that
provided    and  



Step 1:  
We have
Step 2:  
Using the Background Information, we have

We have

Final Answer:  

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