6. At time t = 0 a tank contains 0.05 lb. of salt dissolved in 100...

 

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6. At time t = 0 a tank contains 0.05 lb. of salt dissolved in 100 gal of water. Assume that water containing 14 lb. of salt per gallon is entering the tank at a rate of 3 gal/min, and that the well-stirred solution is leaving the tank at the rate of 3.5 gal/min. Let Q(t) be the number of pounds of salt in the tank at time t min. Find the Volume rate of change. Find the Volume function. Find the domain of the equation, based on the volume function. Find the soluble amount rate in (pounds per minute) (On Paper) Find the differential equation for the net rate of change of the soluble a. b. C. d. e. amount. f. g. h. i. Use the ODE from part d. to find the coefficient of the x² term in the Taylor series (On Paper) Use Integrating factors to find the solution. (On Paper) Find the derivative of the solution, and check that it satisfies the ODE. Find when the maximum amount of salt is in the tank. a. What is dv/dt? (In gallons per minute) 6. At time t = 0 a tank contains 0.05 lb. of salt dissolved in 100 gal of water. Assume that water containing 14 lb. of salt per gallon is entering the tank at a rate of 3 gal/min, and that the well-stirred solution is leaving the tank at the rate of 3.5 gal/min. Let Q(t) be the number of pounds of salt in the tank at time t min. Find the Volume rate of change. Find the Volume function. Find the domain of the equation, based on the volume function. Find the soluble amount rate in (pounds per minute) (On Paper) Find the differential equation for the net rate of change of the soluble a. b. C. d. e. amount. f. g. h. i. Use the ODE from part d. to find the coefficient of the x² term in the Taylor series (On Paper) Use Integrating factors to find the solution. (On Paper) Find the derivative of the solution, and check that it satisfies the ODE. Find when the maximum amount of salt is in the tank. a. What is dv/dt? (In gallons per minute)