This is a Calculus 2 problem.

8. (10 pts) Mixing problem: Dialysis treatment removes urea (or other waste products) from a patient's body by diverting some blood flow to a filter that completely filters out the urea such that a clean blood flow (without urea) is channelled back into the patient while the patient's total blood volume is kept constant. An average individual has 5 liters of blood and a standard dialysis flow is 2 liters per minute. Suppose that the patient starts the dialysis treatment with a concentration of urea of 3 grams/liter. Write a differential equation & its initial condition i.e. the total amount of urea (in grams) in the patient at the beginning of the dialysis] for the TOTAL AMOUNT OF UREA in the patient y(t) (in grams) as a function of time t (in minutes). DE: , IC: ) Find the general solution to this differential equation. y(0) = :) Find the particular solution satisfying the initial condition. y(t) = d) (i) Draw a sketch for the direction field y (g) 20 f the differential equation you found in (a) id (ii) include a sketch (in bold) of the 15- lution you obtained in (c) above. e) [extra credit] 10 i) What is the amount of urea (in grams) left in- side the patient after 1/2 hour of dialysis? 5 'ii) How long would it take for the amount of urea to be half of the amount before treatment? (iii) According to the solution found in (c), how t (min)