Answer
$P^{\prime}(t)=-10t+75$
$P^{\prime}(6)=15$
In the year 2006 the median home price was increasing at a rate of $ 15,000/year.
Work Step by Step
$P^{\prime}(t)=-5(2t)+75(1)-0$
$P^{\prime}(t)=-10t+75$
$P^{\prime}(6)=-10(6)+75=15$
for t=$6$, the year is $2000+6=2006$
$P(c)$ is the rate of change of $P(x)$ when $x=c$,
so our interpretation of $P^{\prime}(6)=15$ is:
In the year 2006 the median home price was increasing at a rate of $ 15,000/year.
