Math  /  Calculus

QuestionAutonomous27: Problem 2 Previous Problem Problem List Next Problem (1 point) Dead leaves accumulate on the ground in a forest at a rate of 3 grams per square centimeter per year. At the same time, these leaves decompose at a continuous rate of 80 percent per year. A. Write a differential equation for the total quantity QQ of dead leaves (per square centimeter) at time tt : dQdt=\frac{d Q}{d t}= \square 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)(t=0) there are no leaves on the ground. What is the initial quantity of leaves? Q(0)=Q(0)= What is the equilibrium level? Qeq=Q_{e q}= \square Does the equilibrium value attained depend on the initial condition? A. yes B. no

Studdy Solution
A. dQdt=30.80Q\frac{dQ}{dt} = 3 - 0.80Q B. Q(0)=0Q(0) = 0 Qeq=3.75Q_{eq} = 3.75 No, the equilibrium value does not depend on the initial condition.

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