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Tues 3/23-Thurs 3/25
During class we worked on several differential equation applications and the problems are shown below. 1. Suppose a deer population grows exponentially at a rate of 10% per year. To keep the population size reasonable, the Park Service removes 20 deer each year. a) Write a differential equation for the rate of change of the size of the deer population with respect to time. b) Solve the differential equation.

2. A chain smoker smokes 5 cigarettes every hour.From each cigarette, 0.4 mg of nicotine is absorbed into the person's bloodstream. Nicotine leaves the body at a rate proportional to the amount present, with constant of proportionality -0.346. a) Write a differential equation for the level of nicotine in the body, N, in mg, as a function of time, t, in hours.

b) Solve the differential equation. Assume that initially there is no nicotine in the blood.

c) The person wakes up at 7 a.m. and begins smoking. How much nicotine is in the blood when the person goes to sleep at 11 p.m.? N(16) = 5.758 so the person has approximately 5.8 mg of nicotine in the blood by 11 pm

3. Dead leaves accumulate on the ground in a forest at a rate of 3 grams per square centimeter per year. At the same time, theses leaves decompose at a continuous rate of 75% per year. Write a differential equation for the total quantity of dead leaves (per square centimeter) at time t. Sketch a solution showing that the quantity of dead leaves tends towards an equilibrium level. What is the equilibrium level?

4 According to a simple physiological model, an athletic adult needs 20 calories per day per pound of body weight to maintain his weight. If he consumes more or fewer than those required to maintain his weight,his weight will change at a rate proportional to the difference between the number of calories consumed and the number needed to maintain his current weight; the constant of proportionality is 1/3500 pounds per calorie. Suppose that a particular person has a caloric intake of I calories per day. Let W(t) be the person's weight in pounds at time t (measured in days). a) What differential equation has solution W(t)? b) Solve this differential equation. c) Draw a graph of W(t) if the person starts out weighing 160 pounds and consumes 3000 calories a day. Label the axes and any intercepts and asymptotes clearly.

Friday 3/26
No class today so we had time to work on the second of our practice AP tests.