Answer
$I(t)=1200t+42,000,$
median household income in 2005$:\quad{{\$}} 48,000$
Work Step by Step
The instaneous rate of change of $I$ is
$I'(t)=1200$
$I(t)=\displaystyle \int(1200)dt=1200t+C$
To find C, use the given information:
$I(0)=42,000$
$42,000=1200(0)+C$
$C=42,000$
$I(t)=1200t+42,000$
The year 2000 is $t=5$ years after 2000.
$I(5)=1200(5)+42,000=48,000$
