In a chemical reactor

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

In a chemical reactor, the concentration

C

of a dissolved substance (in mol/L) depends on the liquid volume

V

(in liters) according to

C(V)=0.50+0.04V^{1/2}

. The reactor is being filled so that the volume after

t

minutes is

V(t)=3t^{2}+4

. Assume both

C

and

V

are differentiable. (a) Calculate

\dfrac{dC}{dt}

t=2

minutes. Include correct units. (b) Interpret the meaning of your result from part (a) in terms of how the concentration is changing in the reactor at that instant.

Related theory

Rates of Change
Advanced Differentiation
Derivatives of standard functions via chain rule
Derivatives of composite functions
Continuity and Differentiability

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