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.
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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.
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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
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