Consider a 50 gallons tank contains 20 gallons of water with 10 pounds of salt m

Question

Consider a 50 gallons tank contains 20 gallons of water with 10 pounds of salt mixed in. Beginning at time t = 0 brine (salt water) with a salt concentration of 1 pound per gallons flows into the tank at a constant rate of 3 gallons per minute and the well-stirred mixture flows out of the tank at the 2 gallons per minute. Let S(t) denote the amass (lbs) of salt in the tank at time t. Write down an initial-value problem that gaverns S(t) (Do not solve). Is the equation in part (a) linear? Seperable? Autonomous? List all the apply.

Explanation / Answer

a)rate of salt inflow =1*3 =3

rate of salt outflow = 2*S/(20+(3-2)t)

rate of change of amount of salt in tank

S'(t)=3 - 2S/(20+t) , S(0)=10

b) equation is linear

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