A 100-gallon tank initially contains 100 gallons of sugar water at a concentration of 0.25 pounds of sugar per gallon. Suppose that sugar is added to the tank at a rate of p pounds per minute, that sugar water is removed at a rate of 1 gallon per minute, and that the water in the tank is kept well mixed. (a) What value of p should we pick so that, when 5 gallons of sugar solution is left in the tank, the concentration is 0.5 pounds of sugar per gallon? (b) Is it possible to choose p so that the last drop of water out of the bucket has a concentration of 0.75 pounds of sugar per gallon?

MATH 1220 Notes for Week #7 22 February 2016 WarmUp ● Remind yourself of the of the statement of the Intermediate Value Theorem (IVT): ○ on a closed interval [a, b] where a < b and f(a) < 0, f(b) > 0, and f is continuous, there exists a number z such that f(z) = 0 ○ note: z is not unique; example is f(x) = sin(x) because sin(x) = 0 on the period kπ Equilibrium...