...
Remember the equation...
$\displaystyle A = A_0e^{kt}$ with $\displaystyle A_0$ being the original amount and k is the rate of growth/decay and t is time.
You know half life means after 5.5 hrs there will be half the substance left so you can....
$\displaystyle .5 = e^{k5.5}$
Because if you put in the values before like....
$\displaystyle 84.8 = 169.6e^{k5.5}$ or even for the original in your part A $\displaystyle 53 = 106e^{k5.5}$ they both will reduce to...
$\displaystyle .5 = e^{k5.5}$
now you need to know the rate, k.
You could make $\displaystyle .5 = e^{k5.5}$ even shorter to begin with, but I think it's important to understand how this came about in case you are given other problems where it's not so cut and dry around half life or exponential growth or decay.
Oh, I forgot to include that once you find k, you can get the equation, with k filled in...
$\displaystyle f(t) = 169.6e^{kt}$