Task 1:

Determine how far \(2^{100} \mathrm{~cm}\) is, to the nearest light year.

Task 2 :

In a couple of paragraphs, describe and react to the issues Verhulst wrote about. Identify key famous people engaged in the debate of his day.

Task 3 :

1. In Equation 1, describe what \(f(0)\) means, and calculate it for Equation 1
2. Now let \(t\) get enormous. Over a very long period of time, what value does \(f(t)\) approach in Equation 1?

Task 4 :

Have at it! Algebraically manipulate Equation 1 until \(e^{-b t}\) is by itself. That is, solve for \(e^{-b t}\). But first, replace \(f(t)\) by \(y\) to simplify the details.

Task 5 :

Scenario 1: Let's assume that \(b=.0075\) and that on Day Zero, there are an estimated 10,000 infected people out of a vulnerable population of 250,000,000.

Scenario 2. Another strain of the flu is more virulent, with double the value of \(b\) as in Scenario 1. Let's also assume 10,000 people have been infected by Day Zero (same vulnerable population).

Scenario 3. Strain 3 is in its second year in the US, so it is estimated that 500,000 people have had that variant. Let us also assume that it was slightly less virulent than the second strain, so that \(k=.008\).

For each of the Scenarios above, determine when half the population \((f(t)=0.5)\) has been infected, and estimate when \(80 \%\) of the vulnerable population has "caught" that strain. Remember, your units for \(t\) are in "days", though that number may be large.

Task 6 :

Using the three Scenarios, compare the impact of the different \(b\) values, and compare the impact of the different \(f(0)\) values. Which factor seems more important-the size of the initial population, or the virulence?

Task 7 :

Assume you start with an initial population of 100,000 infectees. Calculate what value of \(b\) will result in \(60 \%\) of the population being infected as of Day 300 .

Price: $12.25

Solution: The downloadable solution consists of 5 pages, 725 words.
Deliverable: Word Document