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Exponential decay

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A leaking oil tank has a capacity of 500 000 liters of oil. The rate of leakage depends on the pressure of oil remaining in the tank and the pressure depends on the height of oil. When the tank is half-full, it loses 20L/min. How long goes it take to lose 15 000L from half-full?

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Solution Summary

This is a problem regarding exponential decay and a leaking oil tank.

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This is a typical exponential decaying phenomenon.
The rate of leakage is proportional to pressure of oil remaining, and therefore proportional to height of oil, and therefore the remaining volume of the oil.
Basic equations are:
dV/dt = -k * V -> Rate is proportional to remaining volume (V)
...

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