Chapter 2.3, Problem 96E

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

Chapter
Section

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem
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The biomass B(t) of a fish population is the total mass of the members of the population at time t. It is the product of the number of individuals N(t) in the population and the average mass M(t) of a fish at time t. In the case of guppies, breeding occurs continually. Suppose that at time t = 4 weeks the population is 820 guppies and is growing at a rate of 50 guppies per week, while the average mass is 1.2 g and is increasing at a rate of 0.14 g/week. At what rate is the biomass increasing when t = 4 ?

To determine

To find:

At what rate the biomass increasing when t = 4

Explanation

Concept used:

Product rule: If f and g are both differentiable, then

ddxfxgx=fxddxgx+gxddxfx

Given:

Bt=Nt*Mt,Â Â Nt=820,Â Â Mt=Â 1.2,Â Â N't=50,Â M't=0.14

Calculation:

Biomass B(t) of a fish population is product of M(t) and N(t). So Bt=Nt*Mt

For time t = 4 weeks, the information provided in the question is,

Â Nt=820,Â Â Mt=Â 1

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