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?
Correct answer:
![](/img/81/exponentialFexsDecay.jpg)
Showing 3 comments:
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
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.
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
https://en.wikipedia.org/wiki/Exponential_decay
https://en.wikipedia.org/wiki/Time_constant
Tips for related online calculators
Our percentage calculator will help you quickly calculate various typical tasks with percentages.
Tip: Our volume units converter will help you convert volume units.
Do you want to convert time units like minutes to seconds?
Tip: Our volume units converter will help you convert volume units.
Do you want to convert time units like minutes to seconds?
You need to know the following knowledge to solve this word math problem:
Units of physical quantities:
Grade of the word problem:
Related math problems and questions:
- In and out
The empty tank is filled in 12 minutes and empty in 16 minutes. If we forget to close the drain, how long does it take to fill? The tank has 1000 liters of volume.
- Water level
To cuboid-shaped poll, bottom size 2m and 3.5m, flows water at a rate of 50 liters per minute. How long will it take for water to reach a level of 50 cm?
- Hectoliters of water
The pool has a total of 126 hectoliters of water. The first pump draws 2.1 liters of water per second. A second pump pumps 3.5 liters of water per second. How long will it take both pumps to drain four-fifths of the water simultaneously?
- Minutes 7177
The tank holds 140 liters of water. It is filled with a tap in 5 minutes, and the drain is emptied in 7 minutes. How long will it take for the empty tank to fill if we open the faucet and drain it?
- Water inlets
An Inlet valve with a flow rate of 12 liters per second is filled tank for 72 minutes. How long does it take to fill the full tank if we open one more such valve half an hour after?
- Delivers 19143
The pump delivers 34 hl of water per minute. How long does it take to fill the tank with a volume of 10m³? Write the result in hours and minutes.
- Delivers 7184
The pump delivers 0.75 hl of water per minute. How long does it take to fill the tank with a volume of 10m³? Write the result in hours and minutes.