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CALCULUS HELP PLEASE IM DESPERATE-WILL AWARD BEST ANSWER?
The graphs to the right are of the following
functions:
P(c)=Pm(c^2/(k^2+c^2), D(c)=rc
*where Pm=5, k=10 and r=1/5
Let c(t) denote the concentration of a substance involved in a chemical reaction such that
dc/dt= P(c) − D(c).
(a) Calculate all steady states of the differential equation.
(b) Determine the stability of each steady state. Explain how you arrived at your conclusion.
(c) If the initial concentration is c(0) = 8, what concentration does c(t) eventually approach?
Please explain your answers so I may understand this unit.
1 Answer
- rotchmLv 73 years ago
Hints:
This is to practice you to understand the questions and to be able to read graphs.
A stability point is such that c'(t) = dc/dt ≈ 0. Thus P(c) - D(c) = 0 thus P(c) = D(c). This means that the stable points are where the two curves are equal (cross each other). Looking at the graph [or solving for c in P(c) = D(c) ] , there are 3 such stable points. What are they?
Then, look before & after these points; this gives the sign of P - D which is the sign of dc/dt, so it gives u info on the type of stability. (you probably seen the horizontal-vertical ray tracing trick for this).
If c = 8 where are you on the graph? Where will this lead you ?
Done!
