# Science:Math Exam Resources/Courses/MATH103/April 2013/Question 07 (a)

MATH103 April 2013
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### Question 07 (a)

Biofuel: Suppose you work at an experimental algae farm where algae is turned into biofuel. The algae grows in tanks at a rate ${\displaystyle \displaystyle \alpha =2}$ and the steady supply of nutrients allows each tank to sustain ${\displaystyle \displaystyle K}$ kilograms of algae.

The rate of change of the total mass of algae, ${\displaystyle \displaystyle M}$, is given by:

${\displaystyle \displaystyle {\frac {dM}{dt}}=2M{\big (}1-{\frac {M}{K}}{\big )}}$.

Find all steady state solutions (equilibria) for this equation.

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