Answer
$I(t)=1500t+57,000,$
median household income in 2005$:\quad{{\$}} 66,000$
Work Step by Step
The instaneous rate of change of $I$ is
$I'(t)=1500$
$I(t)=\displaystyle \int(1500)dt=1500t+C$
To find C, use the given information:
$I(0)=57,000$
$57,000=1200(0)+C$
$C=57,000$
$I(t)=1500t+57,000$
The year 2006 is $t=6$ years after 2000.
$I(5)=1500(6)+57,000=66,000$
