Dead Leaves Accumulate On The Ground In A Forest At A Rate Of 5 Grams Per Square Centimeter Per Year At The Same Time 1 (44.76 KiB) Viewed 58 times
Dead leaves accumulate on the ground in a forest at a rate of 5 grams per square centimeter per year. At the same time, these leaves decompose at a continuous rate of 85 percent per year. A. Write a differential equation for the total quantity of dead leaves (per square centimeter) at time t: del = 0 B. Sketch a solution to your differential equation showing that the quantity of dead leaves tends toward an equilibrium level. Assume that initially (t = 0) there are no leaves on the ground. What is the initial quantity of leaves? Q(0) What is the equilibrium level? Qeq =
According to a simple physiological model, an athletic adult male needs 20 calories per day per pound of body weight to maintain his weight. If he consumes more or fewer calories than those required to maintain his weight, his weight changes 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 constant caloric intake of H 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)? dW dt (Your answer may involve W, H and values given in the problem.) (b) Solve this differential equation, if the person starts out weighing 165 pounds and consumes 3400 calories a day. W (c) What happens to the person's weight as t→∞? W →
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