009A Sample Final 3, Problem 8

Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure  $P$  and volume  $V$  satisfy the equation  $PV=C$  where  $C$  is a constant. Suppose that at a certain instant, the volume is  $600{\text{ cm}}^{3},$  the pressure is  $150{\text{ kPa}},$  and the pressure is increasing at a rate of  $20{\text{ kPa/min}}.$  At what rate is the volume decreasing at this instant?

Foundations:
Product Rule
${\frac {d}{dx}}(f(x)g(x))=f(x)g'(x)+f'(x)g(x)$

Solution:

Step 1:

Step 2:

Final Answer:

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