If our mathematical model for the decay of a bacteria colony is:
$100\left (\frac {1} {2} \right) ^ {n-1}$ =Number of Bacteria
n is the number of the elapsed hours starting with 100 bacteria in a Petri dish, Such that $ n\geq 1$
Then according to our model, after 6hrs our Petri dish should only contain 3.125 live bacteria. However this doesn't make much sense; we should only have a whole number of live bacteria at any given moment. How does this real world constraint on the mathematical model help solve:
$100\left (\frac {1} {2} \right) ^ {n-1}$ = 0
In general a mathematical model is not able to completely describe every aspect of a system with $100\%$ accuracy. The idea of mathematical modeling is to make a model that is "good enough" for whatever it is modeling. For the case of modeling bacteria, note that there are usually enormous numbers of bacteria in a petri dish, perhaps on the order of billions. So when a biologist wants to know how many bacteria are in the dish, it makes very little difference whether there are say $1,000,000,000$ or $1,000,000,001$. Thus the choice was made to represent the number of bacteria using a continuous rather than discrete value, even though there can never be a fractional amount of bacteria. Now you could do an arithmetic operation such as a floor or ceiling function to give yourself an integer number of bacteria, but this is not really relevant or necessary when "ballparking" a solution by using the model.
As for the equation $100(\frac{1}{2})^{n-1} = 0$, note that this is never zero for any positive value of $n$. However $\lim_{n \to \infty} 100(\frac{1}{2})^{n-1} = 0$, and you can interpret this as all of the bacteria dying after a long amount of time.
The reason that this example seems strange is that this model is being applied to a tiny sample of bacteria. However also notice that if $n$ is the number of elapsed hours, then the initial number of bacteria is actually $100*(\frac{1}{2})^{-1} = 200$, not $100$. (Just plug in $n = 0$).