Assume there is a certain population of fish in a pond whose growth is described by thelogistic equation. It is estimated that the carrying capacity for the pond is 1100 fish. Absentconstraints, the population would grow by 210% per year.If the starting population is given by po = 400, then after one breeding season thepopulation of the pond is given byP1 =After two breeding seasons the population of the pond is given byP2 =Submit Questionesctab2.caps lockshifti1F1F280F3aF4#372$4ヘ6olo 50%F6F7DIIF887&00 *8QWERTYUANSfnTcontroloptionDLLFGHXCVBNHcommand

The logistic growth model is often used to describe how populations grow when there are limits, such…

Answered: Assume there is a certain population of…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 16EQ

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A=A0e^kt 2006 population (millions) Projected 2029 population (millions) Projected growth rate K 46.5 42.7
a conservation group releases 100 toads into a wetlands. after observing the toads for a number of years the estimate number of toads follows the equation p(t)=1000/1+9e^-0.165t, where t is the number of years since the release. a) how many toads are there after 5 years? b) when will the number of toads be 650? c) how many toads will be in the wetlands when their numbers are increasing most rapidly? d) what is the carrying capacity for the number of toads in this wetland? e)sketch a graph of the function. label your axis.
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For letters B and C, use the logistic model P(t) =C/1+Ae^-kt 1. First, estimate the carrying capacity for the US population. Your estimate should be400 million or above (note that there are no incorrect answers). Use this estimatecombined with the fact that the US population was 280 million in 2000 to determinethe constants,AandC, in the logistic model for the population. The starting yearshould be 2000. (a)-Use the fact that the US population was 310 million in 2010 to determine the growthconstant,k, in your logistic model. (b)-Find the US population in 2050. (C)-Find when the US population will be more than 350 million.

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