A 100 gallon tank is filled with a salt solution containing 10 lbs of salt. Pure water is pumped in at a rate of 5 gallons per minute and pumped out at the same rate. How many minutes will it take the amount of salt to drop to 2 lbs

OUR ANSWER IS  4.46  WHICH IS APPROXIMATELY 4.5

Explanation:

check to see how much salt is coming in and going out. Since pure water contains no salt, and the 5 gallons leaving contain 5/100 of the salt present, we have

ds/dt = 5/100 * 0 - 5/100 s

ds/dt = -1/20 s

ds/s = -1/20 dt

s = c*e^(-t/20)

Since s(0) = 10,

s = 10*e^-(t/20)

so, let's find t when s=8

10 e^(-t/20) = 8

e^(-t/20) = 0.8

-t/20 = ln0.8

t = -20 ln0.8 = 4.46

=4.5

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