Water temperature (in ) at a point in a reservoir depends on depth (in meters) by

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

Water temperature (in

^{\circ}\text{C}

) at a point in a reservoir depends on depth

y

(in meters) by

T(y)=20-0.5y

. Depth depends on volume

V

(in m

^{3}

) through

y(V)=(3V)^{1/3}

. The volume of the reservoir is decreasing at a constant rate of

\dfrac{dV}{dt}=-2\text{ m}^{3}\!/\text{min}

. (a) Derive an expression for

\dfrac{dT}{dt}

in terms of

V

and

\dfrac{dV}{dt}

. (b) Evaluate

\dfrac{dT}{dt}

when

V=8\text{ m}^{3}

, including units.