2. A scientist is doing an experiment on the growth of the corona virus. He started the experiment with 106 virus particles. After 14 days, he observed that the number of virus particles reached 107. After a few more days, the scientist observed that the number of virus had reached an equilibrium and is not changing any more. That final number of virus particles was recorded to be 10°. The scientist then assumed that the virus must follow a logistic growth model given by the following differential equation. From these data, determine the value of a.

2. A scientist is doing an experiment on the growth of the corona virus. He started the experiment with 106 virus particles. After 14 days, he observed that the number of virus particles reached 107. After a few more days, the scientist observed that the number of virus had reached an equilibrium and is not changing any more. That final number of virus particles was recorded to be 10°. The scientist then assumed that the virus must follow a logistic growth model given by the following differential equation. From these data, determine the value of a.

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

2. A scientist is doing an experiment on the growth of the corona virus. He
started the experiment with 106 virus particles. After 14 days, he observed
that the number of virus particles reached 107. After a few more days, the
scientist observed that the number of virus had reached an equilibrium and
is not changing any more. That final number of virus particles was recorded
to be 10°. The scientist then assumed that the virus must follow a logistic
growth model given by the following differential equation. From these data,
determine the value of a.

[You can directly use the solution of the logistic model from class lecture. You
don't need to show the solution of the model.
dP
Logistic model:
= aP(1 – P/K) where a and K are constants and P(t)
dt
denotes the population after t days.]

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