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Suppose that the rate at which body weight W changes with age t is x Wa, where a > 0 is a coefficient that takes different values for different species of animal. dW dt 1 dW Write down a W dt (a) The relative growth rate (percentage weight gained per unit of time) is defined as G(W) = formula for G(W). For which values of a is the relative growth rate increasing, and for which values is it decreasing? (b) As fish grow larger, their weight increases each day but the relative growth rate decreases. If the rate of growth is described by xx wa, explain what constraints must be imposed on a. dW dt (a) Write down a formula for G(W). Let k be a constant of proportionality where k>0. G(W) = K (

Suppose that the rate at which body weight W changes with age t is x Wa, where a > 0 is a coefficient that takes different values for different species of animal. dW dt 1 dW Write down a W dt (a) The relative growth rate (percentage weight gained per unit of time) is defined as G(W) = formula for G(W). For which values of a is the relative growth rate increasing, and for which values is it decreasing? (b) As fish grow larger, their weight increases each day but the relative growth rate decreases. If the rate of growth is described by xx wa, explain what constraints must be imposed on a. dW dt (a) Write down a formula for G(W). Let k be a constant of proportionality where k>0. G(W) = K (

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter5: A Survey Of Other Common Functions
Section5.3: Modeling Data With Power Functions
Problem 3TU
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Suppose that the rate at which body weight W changes with age t is x Wa, where a > 0 is a coefficient that takes different values for different species of animal. dW dt 1 dW Write down a (a) The relative growth rate (percentage weight gained per unit of time) is defined as G(W) = - W dt formula for G(W). For which values of a is the relative growth rate increasing, and for which values is it decreasing? (b) As fish grow larger, their weight increases each day but the relative growth rate decreases. If the rate of growth is described by xx wa, explain what constraints must be imposed on a. dW dt (a) Write down a formula for G(W). Let k be a constant of proportionality where k > 0. G(W) = k
Transcribed Image Text:Suppose that the rate at which body weight W changes with age t is x Wa, where a > 0 is a coefficient that takes different values for different species of animal. dW dt 1 dW Write down a (a) The relative growth rate (percentage weight gained per unit of time) is defined as G(W) = - W dt formula for G(W). For which values of a is the relative growth rate increasing, and for which values is it decreasing? (b) As fish grow larger, their weight increases each day but the relative growth rate decreases. If the rate of growth is described by xx wa, explain what constraints must be imposed on a. dW dt (a) Write down a formula for G(W). Let k be a constant of proportionality where k > 0. G(W) = k
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