dL dt k(39-L(t)) with L(0) = 5 (a) Solve the differential equation. (b) Use your solution in (a) to determine k under the assumption that L(2) = 17. Choose the graph that most resembles L(t) for this value of k (c) Find the length of the fish when t = 10. (d) Find the asymptotic length of the fish; that is, find lim→∞L(t). (a) L(t)= 39-34e-kt (b) k= (Type an integer or decimal rounded to three decimal places as needed.). ...

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
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Denote by L(t) the length of a fish at time t, and assume that the fish grows according to von Bertalanffy's equation.
dL
dt
=k(39-L(t)) with L(0) = 5
(a) Solve the differential equation.
(b) Use your solution in (a) to determine k under the assumption that L(2) = 17. Choose the graph that most resembles L(t) for this value of k.
(c) Find the length of the fish when t = 10.
(d) Find the asymptotic length of the fish; that is, find lim→∞L(t).
(a) L(t)= 39-34e¯kt
(b) k =
(Type an integer or decimal rounded to three decimal places as needed.)
Transcribed Image Text:Denote by L(t) the length of a fish at time t, and assume that the fish grows according to von Bertalanffy's equation. dL dt =k(39-L(t)) with L(0) = 5 (a) Solve the differential equation. (b) Use your solution in (a) to determine k under the assumption that L(2) = 17. Choose the graph that most resembles L(t) for this value of k. (c) Find the length of the fish when t = 10. (d) Find the asymptotic length of the fish; that is, find lim→∞L(t). (a) L(t)= 39-34e¯kt (b) k = (Type an integer or decimal rounded to three decimal places as needed.)
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