A tank contains 200 gallons of water and 50 oz of salt. Water containing a salt

Question

A tank contains 200 gallons of water and 50 oz of salt. Water containing a salt concentration of (1/5)(1+(1/5)sin(t)) oz/gal flows into the tank at a rate of 3 gal/min, and the mixture in the tank flows out at the same rate.

The long-time behavior of the solution is an oscillation about a certain constant level. What is this level? What is the amplitude of the oscillation?

Round the values to two decimal places.

A tank contains 200 gallons of water and 50 oz of salt. Water containing a salt concentration of E(1 Esint) oz/gal fl ows into the tank at a rate of 3 gal/min, and the mixture in the tank flows out at the same rate The long-time behavior of the solution is an oscillation about a certain constant level. What is this level? What is the amplitude of the oscillation? Round the values to two decimal places. oscillation about a level OZ Amplitude of the oscillation OZ

Explanation / Answer

The concentration you begin with is 50/200= (1/4)= 0.25 oz/gal
The amplitude of the function 1/5(1+(1/5)sin(t)) is 1/25, considering the ymax=4/25 and ymin=3/25 (you can see this if you plot the function).
It affects the beginning concentration 3/200, because it's 3/200 times smaller so... (this is only after one minute)

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