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?


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


p1=7%=7100=0.07 q=1p1=10.07=93100=0.93 V1=55 l V2=V1 q=55 0.93=102320=51.15 l V3=V2 q=51.15 0.93=47.5695 l V4=V3 q=47.5695 0.9344.2396 l V5=V4 q=44.2396 0.9341.1429 l  V(n)=V(n1) q V(n)=V1 et/τ q=et/τ  τ=1/ln(q)=1/ln(0.93)13.7797 min  Vn0  t=
t2=1/p1=1/0.07=1007=14.2857 min

We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!

Showing 3 comments:
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.

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




Tips to related online calculators
Our percentage calculator will help you quickly calculate various typical tasks with percentages.
Tip: Our volume units converter will help you with the conversion of volume units.
Do you want to convert time units like minutes to seconds?

Next similar math problems:

  • Std-deviation
    standard-dev Calculate standard deviation for file: 63,65,68,69,69,72,75,76,77,79,79,80,82,83,84,88,90
  • Water reservoir
    nadrz_17 One drain hole emptied the water from the tank for 20 hours, with the second drain for 30 hours. How long will the water drain from this tank if we open two drains simultaneously?
  • Pouring alcohol
    roztoky 100 liters of alcohol has 70% How many liters of water need to be added to have 60% alcohol?
  • The crime
    crime The crime rate of a certain city is increasing by exactly 7% each year. If there were 600 crimes in the year 1990 and the crime rate remains constant each year, determine the approximate number of crimes in the year 2025.
  • Savings
    penize_5 Suppose on your 21st birthday you begin making monthly payments of $500 into an account that pays 8% compounded monthly. If you continue the payments untill your 51st birthday (30 years), How much money will be in your account? How much of it is interest?
  • Crystal
    crystal The crystal grows every month 1.2 permille of its mass. For how many months to grow a crystal from weight 177 g to 384 g?
  • To the cinema
    tree Jane at 8 am got message that all 1093 school pupils will go to the cinema. Within 20 min she said it to the three friends. Each of them again for 20 minutes said to the other three. In this way the message spread further. At what time all the children in
  • Sequence
    seq Calculate what member of the sequence specified by ? has value 86.
  • Alcohol 2
    alko Two types of alcohol one 63% and second 75% give 20 liters of 69% alcohol. How many liters of each type are in the mixture?
  • Annual income
    income The annual incomes (in thousands of $) of fifteen families is: 60, 80, 90, 96, 120, 150, 200, 360, 480, 520, 1060, 1200, 1450, 2500, 7200 Calculate harmonic and geometric mean.
  • Hot air balloon
    balon Hot air balloon ascends 25 meters up for a minute after launch. Every minute ascends 75 percent of the height, which climbed in the previous minute. a) how many meters ascend six minutes after takeoff? b) what is the overall height 10 minutes after launch
  • Geometric sequence
    cralici In the geometric sequence is a4 = 20 a9 = -160. Calculate the first member a1 and quotient q.
  • Population growth
    exp_growth How many people will be on Earth from two people for 5,000 years, if every couple has always 4 children, (2 boys and 2 girls) at the age of 25-35, and every man will live 75 years?
  • Sum of series
    question Determine the 6-th member and the sum of a geometric series: 5-4/1+16/5-64/25+256/125-1024/625+....
  • Alcohol mixing
    roztoky_1 How much 64% of the alcohol must be poured into 6 liters of 85% alcohol to produce 79% alcohol?
  • Alcohol
    no_alcohol How many 55% alcohol we need to pour into 14 liters 75% alcohol to get p3% alcohol? How many 65% alcohol we get?
  • Chess
    sachovnica How many ways can select 4 fields on classic chess board with 64 fields, so that fields don't has the same color?