Question

According to Boyle’s law, for a certain gas, pressure an volume are inversely proportional: P = 800/V where V is measured in and pressure P in pounds per square inch.
a) Find the rate of change of P when V=20 , and interpret its meaning (carefully state the units).
b) Find the average rate of change of P when V changes from 20 to 25 . Compare your result with a).

Answer 1

Gicen expression  

a) To find rate of change of P, we take derivative of both sides with respect to v

so we get,

At v= 20, we get rate of change of P as

dP/dV= -2 lb/in^5

This means pressure decraesing at the rate of -2 lb/in^5 when v=20

b) Average rate of change is given by the formula

P(25) = 800/25 = 32

P(20) =800/20 = 40

So average rate would be

Comparing this result with part a , we see that average rate is less than instant rate .