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Math
CalculusCalculus (MindTap Course List)8th Edition

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Chapter 6.3Star, Problem 104E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

Solutions

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Problem 94E
Problem 95E
Problem 96E
Problem 97E
Problem 98E
Problem 99E
Problem 100E
Problem 101E
Problem 102E
Problem 103E
Problem 104E
Problem 105E
Problem 106E
Problem 107E
Problem 108E
Problem 109E
Problem 110E
Problem 111E
Problem 112E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

The rate of growth of a fish population was modeled by the equation

G ( t ) = 60 , 000 e − 0.6 t ( 1 + 5 e − 0.6 t ) 2

where t is measured in years and G in kilograms per year. If the biomass was 25, 000 kg in the year 2000, what is the predicted biomass for the year 2020?

To determine

To find : The biomass for the year 2020, given G(t)=60000e−0.6t(1+5e−0.6t)2

Explanation

Given that the biomass is 25,000 kg in the year 2000.

The growth rate of a fish population was modeled by the equation G(t)=60000e−0.6t(1+5e−0.6t)2 where t is measured in years and G in kilograms per year.1 The units on the growth rate function are kg per year and the units on t (and then ∆t and dt) are years, so the integral will give the net change in kg per year /years = kg from 2000 to 2020.

The net change from 2000 to 2020 = ∫02060000e−0.6t(1+5e−0.6t)2dt

Let u=1+5e−0.6t,then  du=5e−0.6t(−0.6)dt=−3e−0.6tdt

When t=0;u=6 and t=20;u=1+5e−0.6(20)=1+5e−12

So we get,

∫02060000e−0

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Chapter 6.3Star,
Problem 103E
Chapter 6.3Star,
Problem 105E
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