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Dead leaves accumulate on the ground in a forest at a rate of 4 grams per square centimeter per year. At the same time, these leaves decompose at a continuous rate of 70 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? Q Does the equilibrium value attained depend on the initial condition? ○ A. yes B. no

Dead leaves accumulate on the ground in a forest at a rate of 4 grams per square centimeter per year. At the same time, these leaves decompose at a continuous rate of 70 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? Q Does the equilibrium value attained depend on the initial condition? ○ A. yes B. no

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Dead leaves accumulate on the ground in a forest at a rate of 4 grams per square centimeter per year. At the same time, these leaves decompose at a continuous rate of 70 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? Q Does the equilibrium value attained depend on the initial condition? ○ A. yes B. no
Transcribed Image Text:Dead leaves accumulate on the ground in a forest at a rate of 4 grams per square centimeter per year. At the same time, these leaves decompose at a continuous rate of 70 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? Q Does the equilibrium value attained depend on the initial condition? ○ A. yes B. no
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