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 of dead leaves (per square centimeter) at time t: da 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? O A. yes OB. no

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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 of dead leaves (per square centimeter) at time t:
da
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? Qeg =
Does the equilibrium value attained depend on the initial condition?
A. yes
OB. no
Transcribed Image Text: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 of dead leaves (per square centimeter) at time t: da 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? Qeg = Does the equilibrium value attained depend on the initial condition? A. yes OB. no
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