2022-094

A cell has an initial amount of \( l_0 \) liters of water inside it. After one hour has passed, the amount of water is \( 3 l_0 / 4 \). If the rate of water usage for the cell’s physiological functions is inversely proportional to the amount of water in the cell, find an equation that allows you to calculate the amount \( L(t) \) of water in the cell at any point \( t \) in time.

Note: Always consider positive values. Consider time measured in hours, and volume in liters.

1. \( L(t) = l_0 \sqrt{16 - 7t} / 4 \)
2. \( L(t) = l_0 (4 - t) / 4 \)
3. \( L(t) = l_0 \sqrt{-7t^2/16 + 1} / 4 \)
4. \( L(t) = l_0 (t^2 + 16) / 16 \)
5. None of the above

Original Idea by Rómulo Condori