Forming equations for exponential growth/decay questions Problem
Dry cleaners use a cleaning fluid that is purified by evaporation and condensation after each cleaning  cycle. Every time the fluid is purified, 2.1% of it is lost. The fluid has to be topped up when half of
the original fluid remains.
a) Create a model which represents this situation.
b) After how many cycles will the fluid need to be topped up?
Progress
I am thinking that I will need to use something like $y=ca^x$ where $c$ is the initial amount and a equals the decay factor.  However I am not certain if this is correct since an initial amount is not given.
$100$ was the first number to come to mind for the initial amount, I just didn't know if it'd have any influence if the number was different for the initial amount just merely because of  part b) asking how many cycles.

Let the initial volume of the container be $V_0$ and the density be $\rho$.
Let the evaporation and condensation be uniform and that 2.1% of the volume is lost everytime the purifying process is over.
Thus the model is $${\rho\times(\dot V_0 - \dot V_1)} = 0.021*\rho\times\dot V_0$$
Cancelling $\rho$, and converting the volumetric rate to volume, 
You get$$ V_1 = V_0 - 0.021V_0 = 0.979V_0$$
After the second cycle, $$V_2 = V_1(1-0.021) = V_0*(0.979)*(0.979) = 0.979^2V_0$$
After n cycles, $$V_n = 0.979^nV_0$$
And if $$V_n = 0.5V_0 => 0.5V_0 = 0.979^nV_0$$
$$log(0.5) = nlog(0.979) => n = \frac{log(0.5)}{log(0.979)}$$
$$n = 32.69 = 33\text{ cycles}$$
