# Science:Math Exam Resources/Courses/MATH101/April 2007/Question 06 (a)

MATH101 April 2007
Other MATH101 Exams

### Question 06 (a)

The population of fish in a lake is m million, where $m=m(t)$ varies with time t measured in years. The number of fish is currently 2 million.

Suppose m satisfies the logistic-growth differential equation

${\frac {dm}{dt}}=16m\left(1-{\frac {m}{4}}\right)$ When will the number of fish equal 3 million? You may use the fact that the general solution to the logistic-growth differential equation $y'=ky(1-(y/K))$ is $y=K/(1+Ae^{-kt})$ where A is constant.

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