# 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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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?

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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)

Step 3

Then we find the integrat...

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