On the last day in August (31st), you notice a few patches of fungus on the leaves of the pumpkin vines in your garden. The area of the fungus is 1 cm squared. Suppose that the area covered by this fungus quadruples every day, and on September 1, the area covered by the fungus is now 4 cm squared.
After how many days will the fungus cover at least 1,000,000 cm^2? Show or explain how you found your answer in the Show Your Work box.