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Algebra I

Activity:

Spreading Doom

Posted on May 27, 2008

Topic: Data Analysis & Statistics

Students explore a geometric sequence that models the spread of the 2004 Mydoom virus. After finding a rule for the sequence, they apply it recursively to extend it and graph the resulting data as a scatterplot. Then they derive, evaluate, and graph an exponential function to model the data.

State Standards Alignment

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Activity Key Steps:

In this activity, students are presented with a scenario about a computer virus named Mydoom which infected millions of computers in 2004. Students will derive an equation to model the spread of Mydoom.

Students use Lists & Spreadsheets application on the TI-Nspire to assist them in their investigation. Column A gives the number of hours since the virus was released. Column B gives the number of emails sent by the virus in that hour.

Using the number of emails sent by Mydoom each hour students form a geometric sequence. They should see that in this type of sequence there is a fixed number called the common ratio and for continuing the sequence each term should be multiplied by 1.8.

Students use the Fill Down command to see the effects of the virus after 10 hours. They create a scatter plot of the data. Students discuss which variable is dependent or independent and the shape of the scatter plot.

Students study the sequence and write a function to model the data. They will see that they can write an exponential expression to match the data and will resemble f(x) = a • b^x.

Students plot their function against the scatter plot using the Plot Function command.

At the end of this activity, students will be familiar with terms such as exponential function, growth factor, and geometric sequence. Students will be able to create a geometric to model data for the nth term and graph the terms of a geometric sequence as a scatter plot. They will also be able to graph an exponential function