A power supply delivers a constant electrical power of to a device

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

Problem

A power supply delivers a constant electrical power of

P=60\text{ W}

to a device. The current

I(t)

drawn by the device is increasing at a rate of

0.10\text{ A/s}

when the current is

3.0\text{ A}

. Let

V(t)

be the voltage across the device so that

P=I(t)V(t)

. (1) Determine the instantaneous rate of change of the voltage

\dfrac{dV}{dt}

at that moment. Include correct units in your answer. (2) Interpret the sign of

\dfrac{dV}{dt}

in the context of how the device’s operating voltage is changing over time.