A computer virus is a malicious program that can cause high levels of destruction to your computer or your mobile device. Even with an antivirus program installed, infections can still spread very rapidly as it is restricted to detecting infections, based on information on previous virus code.A team of experts wants to study a recently discovered computer virus by building a mathematical model that predictsthe spread of infection,even with an antivirus installed, as a function of time.

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 the first letter of your last name, 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.

Using the function that you have created from #1, find the value of S(9).

Find S'(t), the derivative of S(t). Simplify your answer.

Find the value ofS'(9).

Interpret the meaning of S(9) andS'(9).

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

Generate a graph for S(t) and S'(t).(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 virusprojected to infect the maximum number of machines? What maximum number of machines is projected to be infected?

At what intervalsis 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?