# Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 02 (d)

MATH102 December 2014
Other MATH102 Exams

### Question C 02 (d)

The graphs to the right show two functions,
Graphs

${\displaystyle P(c)=P_{m}{\frac {c^{2}}{k^{2}+c^{2}}},\quad D(c)=rc}$ where ${\displaystyle P_{m}=5}$, ${\displaystyle k=10}$ and ${\displaystyle r=1/5}$. Suppose that ${\displaystyle c(t)}$ is the concentration of a substance involved in a chemical reaction and satisfies the equation ${\displaystyle {\frac {dc}{dt}}=P(c)-D(c).}$

Suppose that ${\displaystyle P_{m}}$ and ${\displaystyle k}$ are as given above. For what value of ${\displaystyle r}$ does the differential equation for ${\displaystyle c(t)}$ have only two steady states?

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