A room with a volume of 5000 ft3 is full of air which contains 2% (CO). Pure air containing no (CO) is pumped into the room at the rate of 200 cubic feet per minute, and the well-mixed air is vented from the room at the same rate. a. Find the equation that models the amount of (CO), x(t), in ft3, which is in the room, as a function of time.  b. How long will it take for the concentration of (CO) in the room to reach 0.01%?

A tank contains 210 liters of fluid in which 50 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 3 L/min; the well-mixed solution is pumped out at the same rate. Let the A(t) be the number of grams of salt in the tank at time t. Find the rate at which the number of grams of salt in the tank is changing at time t.     Find the number A(t) of grams of salt in the tank at time t.

At what speed should a fish swim upstream so as to reach its destination with the least expenditure of energy? The energy depends on the friction of the fish through the water and on the duration of the trip. If the fish swims with velocity v, the energy has been found experimentally to be proportional to (for constant k > 2) times the duration of the trip. A distance of s miles against a current of speed c requires time -c (distance divided by speed). The energy required is then proportional to k = 3, minimizing energy is equivalent to minimizing |- v³ E(v) = = V C vk s v-c. For Find the speed v with which the fish should swim in order to minimize its expenditure E(v). (Your answer will depend on c, the speed of the current.)

2. Caffeine is eliminated from the body at a continuous rate of approximately 17% per hour. A standard cup of coffee contains 150mg of caffeine.  a) Write a formula for the amount of caffeine C in mg as a function of the number t of hours after drinking a cup of coffee.  b) Find the number of hours (to the nearest hour) it makes for half of the caffeine from a cup of coffee to be eliminated from the body.  c) Find the number of hours (to the nearest hour) it takes for only 1.5mg of the caffeine from a cup of coffee to remain in the body.