. Wildlife biologists are studying the fish population of a lake which isstocked with a specific number of fish every year. They discover thatthe fish population, P (in thousands), is well-nodeled by a differentialequation, where t represents time, in years. A slope field for thisdifferential equation is shown to the right. The wildlife biologists areinterested in understanding how the fish population will behave basedon various starting populations and have hired you as a mathematicalconsultant. Write a report to the biologists that specifically addressesthe following questions:10//8.イブブ /ブ/ノ///471/1 ブブノィイ• What, if any, starting populations lead to a die off?• What, if any, starting populations lead to a population explosionto infinity?• What, if any, starting populations lead to a stabilizing of thepopulation?24ーーイイイイ1.1///////1/////////////////////////246.8.Make sure to indicate why and how you reached each conclusion based on the slope field. Your report shoulduse complete sentences and be written in a form that is appropriate to your audience, meaning that it shouldexplain the meaning of the mathematics in layman's terms. You will be graded on how clearly, completely,and convincingly you make your case.

From the given figure, We observe that there are 2 equilibrium lines(0 slope lines), P=3 and P=7

Wildlife biologists are studying the fish population of a lake which is stocked with a specific number of fish every year. They discover that the fish population, P (in thousands), is well-nodeled by a differential equation, where t represents time, in years. A slope field for this differential equation is shown to the right. The wildlife biologists are interested in understanding how the fish population will behave based on various starting populations and have hired you as a mathematical consultant. Write a report to the biologists that specifically addresses the following questions: P 10 ////// ////////// /// 8 7- 4 3 2 • What, if any, starting populations lead to a die off? • What, if any, starting populations lead to a population explosion to infinity? • What, if any, starting populations lead to a stabilizing of the population? 2 6.

Wildlife biologists are studying the fish population of a lake which is stocked with a specific number of fish every year. They discover that the fish population, P (in thousands), is well-nodeled by a differential equation, where t represents time, in years. A slope field for this differential equation is shown to the right. The wildlife biologists are interested in understanding how the fish population will behave based on various starting populations and have hired you as a mathematical consultant. Write a report to the biologists that specifically addresses the following questions: P 10 ////// ////////// /// 8 7- 4 3 2 • What, if any, starting populations lead to a die off? • What, if any, starting populations lead to a population explosion to infinity? • What, if any, starting populations lead to a stabilizing of the population? 2 6.

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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

. Wildlife biologists are studying the fish population of a lake which is
stocked with a specific number of fish every year. They discover that
the fish population, P (in thousands), is well-nodeled by a differential
equation, where t represents time, in years. A slope field for this
differential equation is shown to the right. The wildlife biologists are
interested in understanding how the fish population will behave based
on various starting populations and have hired you as a mathematical
consultant. Write a report to the biologists that specifically addresses
the following questions:
10//
8.
イ
ブブ /
ブ/ノ///
4
71/1 ブ
ブノィ
イ
• What, if any, starting populations lead to a die off?
• What, if any, starting populations lead to a population explosion
to infinity?
• What, if any, starting populations lead to a stabilizing of the
population?
24ーーイイイイ
1.
1///////
1///
///////////////////
///
2
4
6.
8.
Make sure to indicate why and how you reached each conclusion based on the slope field. Your report should
use complete sentences and be written in a form that is appropriate to your audience, meaning that it should
explain the meaning of the mathematics in layman's terms. You will be graded on how clearly, completely,
and convincingly you make your case.

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