You will want to change the water every week, not every 2 weeks.
They tell you to use one filter per month but truth is that the carbon in the filter gets saturated with the chemicals it claims to absorb within about 6 days, and therefore stops absorbing. So really, you ony have to change the cartridge when it's falling apart unless you are really set on changing it every 6 days. They only say every 30 days because that is the easiest way to make the most money. If they were honest and admitted that the carbon deactivates after several days, well... nobody would buy a filter that they have to change every 6 days! So they just say every month and that way they still have you buying their filters.
If you want you could macgyver a filter cartridge out of sponge. I do so by cutting the frame out of the fiter cartridge and then attachign some open-pore sponge.