After how many days is the virus projected to infect the maximum number of machines? What maximum number of machines is projected to be infected?

Be sure to show your work details for all calculations and explain in detail how the answers were determined for critical thinking questions.

Set up a function for the spread of this new computer virus by choosing a value for A, based on using the letter T, from the table below. (A does not necessarily have to be a whole number). In your equation, S(t) is the number of machines projected to be infected and t is the time, in days.

First letter of your last name	Mathematical Model	Possible values for A
A–F		101–120
G–L	,	121–140
M–R		141–160
S–Z		161–180

Using the tangent line approximation method, find the projected number of machines that will be infected after 10 days.

Generate a graph for S(t) and . (There are free downloadable programs like Graph 4.4.2 or Mathematics 4.0; or, there are also online utilities such as this site and many others.) Insert the graph into your Word document that contains all of your work details and answers. Be sure to label and number the axes appropriately. (Note: Some graphing utilities require that the independent variable must be “x” instead of “t”.)

After how many days is the virus projected to infect the maximum number of machines? What maximum number of machines is projected to be infected?

At what intervals is the function increasing and decreasing? What do you think is the reason why the number of infected machines will start to decrease at some point in the domain?

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