Question

Dead leaves accumulate on the ground in a forest at a rate of 2 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 Q of dead leaves (per square centimeter) at time t:

dQ/dt =

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 =

Does the equilibrium value attained depend on the initial condition?
A. yes
B. no

Answer 1