An industrial oven is programmed so that the humidity (in %) should decrease with the…

MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

An industrial oven is programmed so that the humidity

y

(in \%) should decrease with the oven temperature

x

(in

^{\circ}

C) at a constant rate of

\dfrac{dy}{dx}=-0.15\,\%\,^{\circ}\text{C}^{-1}

when the temperature is around

180^{\circ}

C. At one moment the temperature is rising at

1.2\,^{\circ}\text{C min}^{-1}

. (i) Determine the rate at which the humidity should be changing with respect to time at that moment, expressing your answer in

\%\,\text{min}^{-1}

. (ii) Comment on the physical meaning of the sign of your answer.