Question

#27 would you try different t values to find H? Or not?

Answer 1

$H=H(t)$ represents the number of households that own ...blah... $t$ years 1996. So $H(0)$ is the number of households in the year 1996; we're told that $H(0)=62$ (since $H$ 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

$H(1)=1.0485H(0)\approx65$

After 2 years, or 1 year after the first year elapses, the number is

$H(2)=1.0485H(1)=1.0485^2H(0)\approx68$

After 3 years,

$H(3)=1.0485H(2)=1.0485^3H(0)\approx71$

and so on, with the general pattern of

$H(t)=1.0485^tH(0)\implies\boxed{H(t)=62\cdot1.0485^t}$

This is the function you're asked to find.