Calculus help! A 100-liter tank initially full of water develops a leak at the bottom. Given that 30% .....
Favorites|Homepage
Subscriptions | sitemap
HOME > Mathematics > Calculus help! A 100-liter tank initially full of water develops a leak at the bottom. Given that 30% .....

Calculus help! A 100-liter tank initially full of water develops a leak at the bottom. Given that 30% .....

[From: ] [author: ] [Date: 11-05-10] [Hit: ]
k = 0,071335.W = 100*e^(-0.W/100 = e^(-0,71335) = 0,W = 49 L = water left after 10 minutes.......
A 100-liter tank initially full of water develops a leak at the bottom. Given that 30% of the water leaks out in the first 5 minutes, find the amount of water left in the tank 10 minutes after the leak develops if the water drains off at a rate that is proportional to the amount of water present.

-
Hello

The loss of water proceeds exponential according to

water(left) = water(initial)*e^(-kt)

find k with the gives data:

70 = 100*e^(-k*5)

0,7 = e^(-k*5)

-5k = ln(0,7) = - 0,3567

k = 0,071335.
------------
Now use k to find the amount of water after 10 minutes:

W = 100*e^(-0.071335*10)

W/100 = e^(-0,71335) = 0,49

W = 49 L = water left after 10 minutes.

Regards
1
keywords: the,Given,leak,liter,water,bottom,develops,of,Calculus,tank,help,at,initially,100,30%,that,full,Calculus help! A 100-liter tank initially full of water develops a leak at the bottom. Given that 30% .....
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .