Science:Math Exam Resources/Courses/MATH110/April 2014/Question 08 (b)
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Question 08 (b) 

Imagine bushbuck antelopes interacting in a montane forest. Let denote the probability that a given antelope is in contact with another antelope. is modelled by the equation where is a constant denoting the corresponding distances of the species, and is a function denoting the density of antelope in the area. Now suppose for a period of time from to . Make a large sketch of the graph of during that period. 
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Hint 

Use the answer you got from the last part. What happens to if ? 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Since we have , in the case where , we get . Hence the probability of interaction is not changing over time. Hence will be the constant function during that time. 