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

MATH110 April 2014
Other MATH110 Exams

### Question 08 (b)

Imagine bushbuck antelopes interacting in a montane forest. Let ${\displaystyle P}$ denote the probability that a given antelope is in contact with another antelope. ${\displaystyle P}$ is modelled by the equation ${\displaystyle P=1-e^{-\pi \rho D^{2}},}$ where ${\displaystyle D}$ is a constant denoting the corresponding distances of the species, and ${\displaystyle \rho }$ is a function denoting the density of antelope in the area.

Now suppose ${\displaystyle \rho '(t)=0}$ for a period of time from ${\displaystyle t=a}$ to ${\displaystyle t=b}$. Make a large sketch of the graph of ${\displaystyle P}$ during that period.

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