In a chemical reactor

MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations

Problem

In a chemical reactor, the concentration

C(t)

of an impurity (in mol/L) satisfies

\frac{dC}{dt}=-0.3C\,(5-C),\quad t\ge 0,

where

t

is measured in minutes. (a) Identify all constant (equilibrium) concentrations predicted by the model. (b) For

C(0)=2

, determine the sign of

\dfrac{dC}{dt}

t=0

and describe the long–term behavior of

C(t)

t\to\infty

. (c) For

C(0)=8

, determine the sign of

\dfrac{dC}{dt}

t=0

and describe the long–term behavior of

C(t)

t\to\infty

. (d) Sketch qualitative solution curves for initial concentrations both below and above the equilibria, labeling arrows to indicate the direction of change over time.

Related theory

Applications
Qualitative Analysis
Differential Equations

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