# Science:Math Exam Resources/Courses/MATH102/December 2015/Question 15

MATH102 December 2015
Other MATH102 Exams

### Question 15

Someone released a group of 10 rabbits on campus and they started reproducing at a rate proportional to the population size with constant of proportionality of 3 per year. After 5 years, the rabbits continued to reproduce in the same manner but a coyote moved in and began eating rabbits at a rate proportional to the population size with a constant of proportionality of 9 per year. The population of rabbits is given by the function

${\displaystyle P(t)={\begin{cases}C_{0}e^{at}&0\leq t<5,\\C_{1}e^{bt}&t\geq 5.\end{cases}}}$

Give values for ${\displaystyle a}$, ${\displaystyle C_{0}}$ , ${\displaystyle b}$, and ${\displaystyle C_{1}}$. Your answers can be in terms of exponentials and/or logarithms.

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