A tank contains 200 gal of fresh water. A solution containing 4 lb/gal of soluble lawn fertilizer runs into the tank at the rate of 1 gal/min, and the mixture is pumped out ofthe tank at the rate of 5 gal/min. Find the maximum amount of fertilizer in the tank and the time required to reach the maximum.

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Asked Jul 27, 2019
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I need help about solving this problem.

a) How do I find the time required to reach the maximum amount of fertilizer in the tank in minutes?

b) What is the maximum amount of fertilizer in the tank in lb?

A tank contains 200 gal of fresh water. A solution containing 4 lb/gal of soluble lawn fertilizer runs into the tank at the rate of 1 gal/min, and the mixture is pumped out of
the tank at the rate of 5 gal/min. Find the maximum amount of fertilizer in the tank and the time required to reach the maximum.
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A tank contains 200 gal of fresh water. A solution containing 4 lb/gal of soluble lawn fertilizer runs into the tank at the rate of 1 gal/min, and the mixture is pumped out of the tank at the rate of 5 gal/min. Find the maximum amount of fertilizer in the tank and the time required to reach the maximum.

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Expert Answer

Step 1

Let F be the amount of fertilizer. In 1 minute 1 gallon of solution comes in and 5 gallons of solution goes out. So net loss per minute is (5-1)=4 gallons. 

After t minutes there will be 200-4t gallons of solution. 

Step 2

The concentration of fertilizer at time t=F/(200-4t)

 Since there are 5 gallons per minute going out, the amount of fertilizer going out is 5 gallons/minute times F/(200-4t) lb/gallon= 5F/(200-4t)

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5F dF =4- dt where F(0)-0 200-4t

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Step 3

Then we find the integrat...

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5F dF -=4-. dt 200-4t dF Or dt 5F =4 200-4t 5 - dt I.F. e200-4t 5 In(200-4t) I.F. e 4 5 IF. (200-4t)

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Math

Calculus

Differential Equations

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