[tex]H=H(t)[/tex] represents the number of households that own ...blah... [tex]t[/tex] years 1996. So [tex]H(0)[/tex] is the number of households in the year 1996; we're told that [tex]H(0)=62[/tex] (since [tex]H[/tex] is the number of households in millions).
At the end of each year, this number increases by 4.85%, i.e. a factor of 1.0485. This means after 1 year, the number of households is
[tex]H(1)=1.0485H(0)\approx65[/tex]
After 2 years, or 1 year after the first year elapses, the number is
[tex]H(2)=1.0485H(1)=1.0485^2H(0)\approx68[/tex]
After 3 years,
[tex]H(3)=1.0485H(2)=1.0485^3H(0)\approx71[/tex]
and so on, with the general pattern of
[tex]H(t)=1.0485^tH(0)\implies\boxed{H(t)=62\cdot1.0485^t}[/tex]
This is the function you're asked to find.
