A tree farm starts with eight trees. Tree growth is expected to follow logistic growth with a first order growth rate constant of r = 0.15 yr–1 to a maximum of 6,000 trees. A. Write the equation that relates the number of trees (N) to time (t). What are the values of N0, r, and K? B. Plot the number of trees over time if no harvesting occurs. Go out to about 80 years. C. What is the maximum sustainable yield (MSY)? How long should you wait before harvesting at the MSY?
A tree farm starts with eight trees. Tree growth is expected to follow logistic growth with a first order growth rate constant of r = 0.15 yr–1 to a maximum of 6,000 trees. A. Write the equation that relates the number of trees (N) to time (t). What are the values of N0, r, and K? B. Plot the number of trees over time if no harvesting occurs. Go out to about 80 years. C. What is the maximum sustainable yield (MSY)? How long should you wait before harvesting at the MSY?
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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A tree farm starts with eight trees. Tree growth is expected to follow logistic growth with a first order growth rate constant of r = 0.15 yr–1 to a maximum of 6,000 trees.
A. Write the equation that relates the number of trees (N) to time (t). What are the values of N0, r, and K?
B. Plot the number of trees over time if no harvesting occurs. Go out to about 80 years.
C. What is the maximum sustainable yield (MSY)? How long should you wait before harvesting at the MSY?
D. What is the standing crop? (The standing crop is the number of trees at steady state when harvesting at the MSY.)
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