In a laboratory experiment

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

Problem

In a laboratory experiment, the concentration yy (mol/L) of a reactant and the temperature xx (∘^{\circ}C) both vary with time. At t=12 t=12\,s the instruments show dydt=−0.25 mol L−1s−1\dfrac{dy}{dt}=-0.25\,\text{mol L}^{-1}\text{s}^{-1} and dxdt=0.50 ∘C s−1\dfrac{dx}{dt}=0.50\,^{\circ}\text{C s}^{-1}. (i) Calculate the instantaneous rate at which the concentration changes with respect to temperature at t=12 t=12\,s. (ii) State the correct units of this rate. (iii) Determine whether the concentration is increasing or decreasing as temperature rises at this instant.

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