Please answer all parts

M = 2000

Introduction: A chemical in a liquid solution (or dispersed in a gas) runs into a container holding the liquid (or the gas) with, possibly, a specified amount of the chemical dissolved as well. The mixture is kept uniform by stirring and flows out of the container at a known rate. In this process, it is often important to know the concentration of the chemical in the container at any given time. The differential equation describing the process is based on the formula: Rate of change of amount in container = rate at which chemical arrives rate at which chemical departs (1) If y(t) is the amount of the chemical in the container at time t and V(t) is the total volume of liquid in the container at time t, then the departure rate of the chemical at time tis Departure rate = ylt) V(t) (outflow rate) Departure rate = (Concentration in container at time t). (out flow rate) Accordingly, Equation (1) becomes dy dt = (chemical's arrival rate) ye) V() (outflow rate)(kg/min) --(4) where Chemical's arrival rate = amount of additive kg litre litre x additive pumped rate into tank in Problem: As an engineer in oil refinery site, your main task is to design equipment that removes the gas and oil from the ground as well as suggest ways to extract gas and oil more effectively. In an oil refinery site, a storage tank contains a total of M litre of gasoline that initially has 5% of M litre of an additive dissolved in it. To prepare for colder weather, gasoline containing 0.1% of M kg of additive per litre is pumped into the tank at the rate of 2% of M litre/min. The well-mixed solution is pumped out at a rate of 2.5% of M litre/min. Note: Refer to Figure 1 for illustration of the situation 2% of M litre/min containing 0.1% of Mkg of additive per litre 2.5% of M liter/min containing kg/Utre Figure 1: The storage tank with the mixes input liquid with stored liquid to produce an output liquid Questions: 1. Determine volume of gasoline and additive (in liter) in solution in the tank at any time t (express your equation in terms of t) 2. Determine the differential equation of the modelling the mixture process (refer to the Equations (1) to (4)). 3. Determine the particular solution of the initial value problem 4. How much of the additive is in the tank 20 minutes after the pumping process begins? 5. Repeat the calculation in (4) to determine the amount of additive in tank from 0 to 40 minutes. Draw plots of amount of additive pumped rate into the tank against the time (from 0 to 40 minutes with the interval of 5 minutes each). From the plotted graph, explain your