5. Suppose that sodium pentobarbital is used to anesthetize a dog. The dog is anesthetized when its bloodstream contains at least 45 milligrams (mg) of sodium pentobarbitol per kilogram of the dog's body weight. Suppose also that sodium pentobarbitol is eliminated from the dog's bloodstream at a rate which is proportional to the amount of sodium pentobarbitol in the bloodstream and that after 5 hours half of the initially prescribed sodium pentobarbitol is elliminated from the bloodstream. Set up and solve an initial value differential equation. What single dose should be administered in order to anesthetize a 50-kg dog for 1 hr?

1. At 12:00 p.m. a tank contains 150 g of salt dissolved in 8 L of water. Pure water begins flowing into the tank at a rate of 2 L per hour and the well-mixed solution flows out of the tank at a rate of 3 L per hour. At What time will the tank contain 100 g of salt (or will the tank empty before this happens)? 2. At 12:00 p.m. the next day, another tank contains 150 g of salt dissolved in 8 L of water. Water containing 10 g of salt per L begins flowing into the tank at a rate of 2 L per hour and the well-mixed solution flows out of the tank at the same rate. At What time will the tank contain 100 g of salt (or will this never happen)?

(b). Consider 2 intercomected tank. Tank A initially contains 18⁰ L of water and log of salt, and tank B Initially contains looL of water and 25g of salt. The Liquid inside each tank is kept well stirred. Liquid flows from tank A to tank B at a rate of BL/min and liquid flows from tank B to tank A at rate of 34lmin. A salt brine with connectration 179/L of salt flows into tank A at a rate of 4 L/min and the solution drains out at 4 L/min. i). Draw a collection of tanks diagram such that all flow rates, volumes, and the incoming salt concentration are shown on it. ii). Write out a system of first-order linear differential equations that would describle the rates of charge of the concentrations of salt, Cilt), (zlt). Do not forget to write the initial conditions. Do not save the equations.

The population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t. After 40 minutes it is observed that 100 bacteria are present. After 1 hour 80 bacteria are present. What was the initial number of bacteria?