Suppose that in Lincoln Park there are 1000 trees, a mixture of maple trees and elm trees. Each year 50 trees (chosen randomly) are removed, and 35 maple trees and 15 elm trees are planted in their place. Suppose that in 2020 the trees in Lincoln Park were half maple 5. trees and half elm trees. (a) Write a differential equation and an initial condition for M(t), the number of maple trees after t years have passed (starting in 2020). (Do not solve the equation.)

Suppose that in Lincoln Park there are 1000 trees, a mixture of maple trees and elm trees. Each year 50 trees (chosen randomly) are removed, and 35 maple trees and 15 elm trees are planted in their place. Suppose that in 2020 the trees in Lincoln Park were half maple 5. trees and half elm trees. (a) Write a differential equation and an initial condition for M(t), the number of maple trees after t years have passed (starting in 2020). (Do not solve the equation.)

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

Suppose that in Lincoln Park there are 1000 trees, a mixture of maple trees and
elm trees. Each year 50 trees (chosen randomly) are removed, and 35 maple trees and 15 elm
trees are planted in their place. Suppose that in 2020 the trees in Lincoln Park were half maple
5.
trees and half elm trees.
(a) Write a differential equation and an initial condition for M(t), the number of maple trees
after t years have passed (starting in 2020). (Do not solve the equation.)
(b) Sketch a direction field for this differential equation, and draw an approximate solution
curve corresponding to the appropriate initial condition.

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