5. Annenberg is serving a tropical juice mix to students. The pineapple-orange-mango mix is stored in a large, well-mixed vat. At 7:00am (t = 0), the vat contains 30 quarts of the mixture, of which 20% is pineapple, 10% is mango and 70% is orange juice. Students are consuming the mix at a rate of 2 quarts per hour, and the vat is being refilled at a rate of 2 quarts per hour with pineapple/mango juice that is one quarter pineapple juice and three quarters mango juice. (a) Write a differential equation whose solution is M = M(t), the number of quarts of mango juice in the container at time t. Include an initial condition. (b) Find the solution to the differential equation and from part (a), with the initial condition you provided. Use your solution to determine what happens to the amount of mango juice in the container in the long run. Why does this result make sense? (c) Suppose that instead, the rate at which people are drinking the juice is 4 quarts per hour. Write a new differential equation reflecting this change. Do you think that this differential equation is separable