Problem

Assume that the pressure exerted by the gas is modeled by the equation

Determine the rates at which the pressure and the volume are changing, with respect to time.

Solution

To find dP/dt, since we are given P(t), just differentiate:

We can find dV/dt in two different ways: either use Boyle's law to find the formula for V(t) and differentiate, or use the equation from example 1,