# Science:Math Exam Resources/Courses/MATH102/December 2015/Question 07

MATH102 December 2015
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### Question 07

Rainbow Trout in Deer Lake can no longer reproduce due to habitat destruction. On November 1st when the population is estimated at 800 fish, locals start stocking the lake with fish at a constant rate of 100 fish per day and fish them out at a rate proportional to their population size. In the options below, ${\displaystyle r>0}$. Which of the following equations describes the size of the fish population?

(a) ${\displaystyle F(t)=100t-800e^{-rt}}$

(b) ${\displaystyle {\frac {dF}{dt}}=(100-r)F}$

(c) ${\displaystyle F(t)=100/r+(800-100/r)e^{-rt}}$

(d) ${\displaystyle {\frac {dF}{dt}}=r(100-F)}$

(e) ${\displaystyle {\frac {dF}{dt}}=100t-rF}$

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