Answer
$S(t)=4.9e^{0.032t}$ million homes
in 2010, $\quad 5.2$ million homes
in 2012, $\quad 5.6$ million homes
Work Step by Step
Continuous growth model:$\quad f(x)=Ae^{rx}$
We use the notation:
$\quad S(t)=S_{0}e^{kt}$
where $S_{0}=4.9,k=0.032, t=$ years after 2008.
Thus, our model is
$S(t)=4.9e^{0.032t}$ million homes
For the year 2010, $t=2$
$S(2)=4.9e^{0.032(2)}\approx 5.22385$
For the year 2012, $t=4$
$S(4)=4.9e^{0.032(4)}\approx 5.56910$
