A bacteria population has logistic growht pattern with initial population 1000 and equilibrium population of 10.000. A count shows that at the end of 1 hour there are 2000 bacteria present. a)Write the initial value problem for the phenomena and determine the population as a function of time. b)Determine the time time at which the population is increasing more rapidly.

A bacteria population has logistic growht pattern with initial population 1000 and equilibrium population of 10.000. A count shows that at the end of 1 hour there are 2000 bacteria present. a)Write the initial value problem for the phenomena and determine the population as a function of time. b)Determine the time time at which the population is increasing more rapidly.

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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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

A bacteria population has logistic growht pattern with initial population 1000 and equilibrium
population of 10.000. A count shows that at the end of 1 hour there are 2000 bacteria present.
a)Write the initial value problem for the phenomena and determine the population as a function
of time.
b)Determine the time time at which the population is increasing more rapidly.

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Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1200 fish. Absent constraints, the population would grow by 110% per year.If the starting population is given by �0=500, then after one breeding season the population of the pond is given by�1 = After two breeding seasons the population of the pond is given by�2 =