# Exponential decay

A tank contains 55 liters of water. Water is flowing out at the rate of 7% per minute. How long does it take to drain the tank?

Result

t = min (Correct answer is: INF)
t2 =  14.2857 min

#### Solution:

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Matematik
t = infinity time to drain at rate 7% per minute of remaining volume. (exponential decay curve never touch  or cross zero - line y=0).  Time constant τ = 13.77 min

t2 = 14.286 min if we took 7% as linear volume decay, but this is not correct in this case.

see more on https://en.wikipedia.org/wiki/Exponential_decay

Math Student
Thank you so much for your assistance.
I tried to solve using geometric sequence.
At t=~13.77 mins, there's ~20.2 liters of water left in the tank.

I do realize that the exponential function will never be zero. However, logically there must be a finite time when the tank will be emptied.
Still can't resolve the situation.

However, thank you again for your time and effort.

Matematik
Yes, the right answer is then: the tank is empty in infinity time... T=13.77 mins is time constant, all decays can be normalized in time to have the same curve, but technically emptied at a time approx. 3-5 time constants. After time constant 13.77 mins the tank is on 63%... etc

https://en.wikipedia.org/wiki/Exponential_decay

https://en.wikipedia.org/wiki/Time_constant

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Tip: Our volume units converter will help you with the conversion of volume units.
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