L(t)LaL (0)iOL(t)LaL (0)i Von Bertalanffy's equation states that the rate of growth in length of an individual fish is proportional to the difference between the current length L and the asymptoticlength La (in centimeters).а(a) Write a differential equation that expresses this idea. (Assume L₂ > L. Use k for the proportionality constant.)adLdt(b) Make a rough sketch of the graph of a solution of a typical initial-value problem for this differential equation.L(t)L(t)LaL (0)OTASL (0)Lai

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Answered: Von Bertalanffy's equation states that…

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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Because of heavy rainfall, the water level in a reservoir is rising at a rate of g(t) feet per hour, where t = 0 corresponds to noon. What does g(t) dt represent?
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According to Newton's law of cooling, the temperature of a body changes at a rate proportional to the difference between the temperature of the body and the temperature of the surrounding medium. Thus, if Tm is the temperature of the medium and T = T(t) is the temperature of the body at time t, then T'= -k(T - Tm) where k is a positive constant. In this exercise, you will verify that T = Tm+ (To-Tm)e -kt is a solution to the differential equation. Here To denotes the initial temperature T(0) of the body. (a) First substitute the above expression for T into the left side of the differential equation. In other words, compute T'. Use an underscore "_" to write the subscripts on To and Im T'= (b) Next substitute the above expression for T into the right side of the differential equation. In other words, compute -k(T – Tm). - -k(T - Tm) (c) Are your answers in parts (a) and (b) equal? No Yes

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