4. During the production process at a local brewery, a batch of beer with 6% alcohol is pumped into a barrel containing a 500 gallon batch of beer with 4% alcohol at a rate of 5 gallons/minute. The resulting mixture is pumped out at the same rate. As the two batches mix, the total volume of pure alcohol in the barrel a(t) changes as a function of time and satisfies the following first-order differential equation and initial condition: a+0.01a(t)=0.3a(0)=20gallonsofalcohol a) Determine the transient solution, atrans(t). (5 points) b) Determine the steady-state solution, ass(t). ( 5 points) c) Determine the total solution a(t), subject to the given initial condition. (5 points) d) Plot a(t) as a function of time for 0