Problem 3: A research group studies the growth of sequoia trees. They are interested in predict- ing the height h(t) (in meters) of a tree depending on its age t (in years). Inspired by the logistic population model, they decided to model the growth of a tree by the differential equation h' = r(1 where r is a growth rate constant that is the same for all sequoias and K is a constant that depends on the environment. h K 1. Suppose that r = 1 and K = 20. What will be the height of a ten years old tree according to this model? Solution: General solution of the equation is h(t) = K+ (h(0) - K)e-kt. So for the given valu (At age zero the tree has height zero), h(10) = 20 - 20e-1.
Problem 3: A research group studies the growth of sequoia trees. They are interested in predict- ing the height h(t) (in meters) of a tree depending on its age t (in years). Inspired by the logistic population model, they decided to model the growth of a tree by the differential equation h' = r(1 where r is a growth rate constant that is the same for all sequoias and K is a constant that depends on the environment. h K 1. Suppose that r = 1 and K = 20. What will be the height of a ten years old tree according to this model? Solution: General solution of the equation is h(t) = K+ (h(0) - K)e-kt. So for the given valu (At age zero the tree has height zero), h(10) = 20 - 20e-1.
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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Transcribed Image Text:Problem 3: A research group studies the growth of sequoia trees. They are interested in predict-
ing the height h(t) (in meters) of a tree depending on its age t (in years). Inspired by the logistic
population model, they decided to model the growth of a tree by the differential equation
h' = r(1
where r is a growth rate constant that is the same for all sequoias and K is a constant that depends
on the environment.
h
K
1. Suppose that r = 1 and K = 20. What will be the height of a ten years old tree according
to this model? Solution: General solution of the equation is
h(t) = K+ (h(0) – K)e-kt.
So for the given values (At age zero the tree has height zero),
h(10) 2020e-1.
=
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