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) Wrong answer
t2 =  14.2857 min

Step-by-step explanation:

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=14.2857 min



Did you find an error or inaccuracy? Feel free to write us. Thank you!



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

#
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

avatar









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?

Related math problems and questions:

  • Chess
    sachovnica How many ways can select 4 fields on a classic chessboard with 64 fields so that fields don't have the same color?
  • Salami
    salama How many ways can we choose 5 pcs of salami if we have 6 types of salami for 10 pieces and one type for 4 pieces?
  • Quiz or test
    test I have a quiz with 20 questions. Each question has 4 multiple choice answers, A, B, C, D. THERE IS NO WAY TO KNOW THE CORRECT ANSWER OF ANY GIVEN QUESTION, but the answers are static, in that if the "correct" answer to #1 = C, then it will always be equal
  • 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
  • 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?
  • You take
    exp_growth You take out Php 20 000 loan at 5% interest rate. If the interest is compounded annually, a. Give an exponential model for the situation b. How much Will you owe after 10 years?
  • Infinity
    circles-and-squares In a square with side 19 is inscribed circle, the circle is inscribed next square, again circle, and so on to infinity. Calculate the sum of the area of all these squares.
  • Wood in the forest
    drevo The amount of wood in the forest was estimated at 6000 m3. How much wood will be in forest after 2 years if the annual growth of wood is 2.5% each year and logging 30 m3 each year?
  • Two cars
    cars_racing Two cars started against each other at the same time to journey long 346 km. The first car went 53 km/h and the second 53 km/h. What distance will be between these cars 20 minutes before meet?
  • Solve 2
    numbers2 Solve integer equation: a +b+c =30 a, b, c = can be odd natural number from this set (1,3,5,7,9,11,13,15)
  • The city 2
    kingkong Today lives 298000 citizens in the city. How many citizens can we expect in 8 years if their annual increase is 2.4%?
  • 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
  • Phone numbers
    old_phone How many 7-digit telephone numbers can be compiled from the digits 0,1,2,..,8,9 that no digit is repeated?
  • Image reduction
    picture2 To say that I am mathematically challenged is a gross understatement! I'm trying to help my friend determine how to calculate percentages of reduction or enlargement for a quilt pattern. She is creating a drawing of a cute picture that will become a piece
  • Vinegar 2
    ocet How many percentages of vinegar solution will we get if we mix 3.5 liters of 5.8% and 5 liters of 7.6% vinegar?
  • Brick wall
    plot_zed Garden 70 m long and 48 m wide should surround with wall 2.1 meters high and 30 cm thick. Wall will be built on the garden ground. How many will we need bricks if to 1 m³ is required approximately 300 bricks?
  • Digits
    pin_keyboard How many odd four-digit numbers can we create from digits: 0, 3, 5, 6, 7? (a) the figures may be repeated (b) the digits may not be repeated