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 50 percent per year. A. Write a differential equation for the total quantity Q of dead leaves (per square centimeter) at time t: 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? OA. yes OB. no

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 50 percent per year. A. Write a differential equation for the total quantity Q of dead leaves (per square centimeter) at time t: 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? OA. yes OB. no

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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

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 50 percent per year.
A. Write a differential equation for the total quantity Q of dead leaves (per square centimeter) at time t:
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? Qea
Does the equilibrium value attained depend on the initial condition?
OA. yes
OB. no

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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
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