When mixing a certain cocktail a barperson starts with a 5 litre solution of 10% alcohol. Into this solution the barperson mixes vodka (40% alcohol) at the rate of 2 litres/minute and pours into glasses at the rate of 3 litres/minute.
a. Find a formula for the volume V(t) of the mixture at time t minutes.
b. Find a differential equation that tells the rate of change of the amount of alcohol A(t) at time t minutes.
c. Solve the differential equation and use the initial condition to find a formula for A(t).