A 200-liter tank initially full of water develops a leak at the bottom. Given that 20% of the water leaks out in the first 5 minutes, find the amount of water leeft in the tank t minutes after leak develops if the water drains off at a rate proportional to amount of water present.
2007-11-02 20:55:39 · 2 answers · asked by Sony55311 1 in Science & Mathematics ➔ Physics
In any system in which the rate of change is proportional to the quantity remaining, the form of the solution is
V = V0*e^-(t/tc)
V0 is the initial volume (200 liters).
Find tc from the fact that at t = 5 minutes, V = 0.8*V0:
0.8*V0 = V0*e^-(5/tc)
ln(0.8) = -5/tc
tc = -5/ln(0.8)
tc = 22.4 min
and the formula is
V = 200*e^-(t/22.4)
2007-11-02 21:22:43 · answer #1 · answered by gp4rts 7 · 0⤊ 0⤋
What is the constant of proportionality?
2007-11-03 10:19:14 · answer #2 · answered by Joymash 6 · 0⤊ 0⤋