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. 6% Alcohol e 5 gal/min Mixture e 5 gal/min 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: da + 0.01a(t) = 0.3 dt a(0) = 20 gallons of alcohol a) Determine the transient solution, atrans(t)

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.