The concentration (in mol/L) of an acid in a cooling reactor is

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

The concentration CC (in mol/L) of an acid in a cooling reactor is C(T)=0.8e−T/15C(T) = 0.8e^{-T/15}, where TT (in °C) is the temperature of the mixture. The temperature declines with time tt (in minutes) according to T(t)=90e−0.04t+30T(t) = 90e^{-0.04t} + 30. (i) Obtain an expression for dCdt\dfrac{dC}{dt} in terms of tt. (ii) Find dCdt\dfrac{dC}{dt} at t=20 mint = 20\,\text{min} and state whether the concentration is increasing or decreasing at that instant.

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