Answer
$P^{\prime}(t)=0.9t-12$
$P^{\prime}(20)=6$
In 2000, the price of a barrel of oil was increasing at a rate of $\$ 6$/year.
Work Step by Step
$P^{\prime}(t)=0.45(2t)-12(1)+0$
$P^{\prime}(t)=0.9t-12$
$P^{\prime}(20)=0.9(20)-12=6$
for t=20, the year is 1980+20=2000
$P(c)$ is the rate of change of $P(x)$ when $x=c$,
so our interpretation of $P^{\prime}(20)=6$ is:
"The rate of change of barrel prices in the year 2000 was $\$ 6$/year ."
or
"In 2000, the price of a barrel of oil was increasing at a rate of $\$ 6$/year."
