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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
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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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.
Transcribed Image Text: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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