Breeding of a certain species of insects is incredible everyday the total number of such insects in a closed glass jar is double the number on the previous day. There was just one insect in the jar on 1/2/2007, and the jar was full to the brim with these insects on 28/2/2007. On which date of February was the jar quarter-full?

### Concept & Logic This is a classic reverse exponential growth problem. If a quantity doubles moving forward in time, it halves moving backward in time. No complex formulas are needed—just logical backtracking. ### Step-by-Step Solution * **Given:** The jar doubles in capacity every single day. The jar is 100% full (1) on February 28, 2007. * **Backtrack one day (Half-full):** On February 27, the jar must have been exactly half-full, because doubling a half-full jar makes it completely full the next day. * **Backtrack a second day (Quarter-full):** On February 26, the jar must have been a quarter-full ($\frac{1}{4}$), because doubling it would make it half-full on the 27th. ### Exam Strategy & Shortcut Whenever a problem asks when a continuously doubling entity was a certain fraction ($\frac{1}{2^n}$) of its final size, simply subtract $n$ units of time from the final date. Quarter-full is $\frac{1}{4} = \frac{1}{2^2}$. Subtract 2 days from the 28th to get the 26th. ### Common Pitfall A common reflexive mistake is to divide the total time by 4 (e.g., 28 / 4 = 7). Exponential growth accelerates rapidly at the end; it spends the vast majority of its time barely filling the jar. Always think backwards from the end state. ### Final Answer **Therefore, the correct answer is 26.**