Quiz

1. Consider the autonomous rst-order differential equation d dy=yy3v yfl=yo 1' Sketch the graph of a typical solution y[;r} when (a) yo = 2 (b) '90 = 2 (C) so = 0-5 ((0 ya = 0-5 2. The population of a certain town doubles in 14 years. How long will it take for the population to triple? Assume that the rate of increase of the population is proportional to the population. 3. Mixture A large tank is lled to capacity with 500 gallons of pure water. Brine solution containing 1 pounds of salt per gallon is pumped into the tank at a rate of 3 gal f min. The well-mixed solution is pumped out at the same rate. (a) Find the number AH) of pounds of salt in the tank at time t (b) Find the concentration c(t} of the salt in the tank is at time t. ((3) Sketch the graph of c{t). (d) 'What is the concentration of the salt after long time? 4. Logistic: The number IVE) of people in a small town who are exposed to a particular. advertisement is governed by the logistic equation. Initially, N(0) = 1000, and it is observed that NH) = 2000. Solve for NIB} if it is predicted that the limiting number of people in the town who will see the advertisement is 100.000