Outbreak Analysis

Epidemiology Department: Graphing Division

Analyst:

Urgent: Situation Briefing

A new digital virus is spreading through the school's server. The number of infected files doubles every hour, modeled by f(x) = 5(2)^x, where x is time in hours.

Threshold One: Security Breach

If the virus infects more than 80 files, the server firewall will fail. Solve the inequality graphically:

5(2)^x > 80

Graphical Sketch Area

Use technology to find the intersection first

Solution in Interval Notation

( ____ , ____ )

Explain what this means in terms of hours:

Threshold Two: Safe Zone

IT can contain the virus only if it is under 320 files. Write and solve the inequality:

Write Inequality

___________

Solution Set

{ x | x < ____ }

Challenge: The Mitigation Window

A special security patch is effective only when the virus has infected between 40 and 160 files. Using your graph, find the exact window of time (in hours) when the patch can be deployed.

[ ____ , ____ ]

Note: Use inclusive brackets [ ] because the patch works at the exact limits.