The von Bertalanffy growth model states that the rate of increase in the length L(t) of a shark of age t in years is proportional to the difference between a fixed maximum length M and its current leng L(t). 1. Write a differential equation (DE) for the length of the shark at any time, using r to represent the proprotional constant. (Hint: your answer should be of the form L'(t) = ....) 2. Explain carefully what this DE predicts would happen if a mutant shark were born with a length larger than M. 3. Show that L(t)= M-(M-Lo)e-t is a solution to the DE in Part 1, where Lo is the length of the shark at time t=0 when it is born. (Hint: if y(t) = A + Bert then y'(t) = -rBe-t.)
The von Bertalanffy growth model states that the rate of increase in the length L(t) of a shark of age t in years is proportional to the difference between a fixed maximum length M and its current leng L(t). 1. Write a differential equation (DE) for the length of the shark at any time, using r to represent the proprotional constant. (Hint: your answer should be of the form L'(t) = ....) 2. Explain carefully what this DE predicts would happen if a mutant shark were born with a length larger than M. 3. Show that L(t)= M-(M-Lo)e-t is a solution to the DE in Part 1, where Lo is the length of the shark at time t=0 when it is born. (Hint: if y(t) = A + Bert then y'(t) = -rBe-t.)
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:The von Bertalanffy growth model states that the rate of increase in the length L(t) of a shark of age t in years is proportional to the difference between a fixed maximum length M and its current length
L(t).
1. Write a differential equation (DE) for the length of the shark at any time, using to represent the proprotional constant. (Hint: your answer should be of the form L'(t) = ....)
2. Explain carefully what this DE predicts would happen if a mutant shark were born with a length larger than M.
3. Show that
L(t) = M – (M — Lo)e¯rt
is a solution to the DE in Part 1, where Lo is the length of the shark at time t = 0 when it is born. (Hint: if y(t) = A + Be¯rt then y' (t) = −rBe¯rt.)
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