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Exponential Growth of Computer Security Incidents from 1996 to 2003

This document examines the exponential growth of computer security incidents, starting with 2,573 incidents reported in 1996. Over the next seven years, incidents increased by approximately 92% annually. The exponential growth model ( n = 2573(1 + 0.92)^t ) is introduced, allowing for estimations of incidents in subsequent years, including approximately 247,485 incidents by 2003. The text also discusses estimating trends through graphical representation, helping visualize the escalating threat of computer viruses and security issues.

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Exponential Growth of Computer Security Incidents from 1996 to 2003

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  1. In 1996, there were 2573 computer viruses and other computer security incidents. During the next 7 years, the number of incidents increased by about 92% each year. Computers EXAMPLE 4 Solve a multi-step problem • Write an exponential growth model giving the number n of incidents tyears after 1996. About how many incidents were there in 2003?

  2. t t = 2573(1.92) n = a(1 + r) t = 2573(1 + 0.92) EXAMPLE 4 Solve a multi-step problem • Graph the model. • Use the graph to estimate the year when there were about 125,000 computer security incidents. SOLUTION STEP 1 The initial amount is a = 2573 and the percent increase is r =0.92. So, the exponential growth model is: Write exponential growth model. Substitute 2573 for aand 0.92 for r. Simplify.

  3. Using this model, you can estimate the number of incidents in 2003 (t = 7) to be n = 2573(1.92) 247,485. 7 EXAMPLE 4 Solve a multi-step problem STEP 2 The graph passes through the points (0, 2573) and (1,4940.16). Plot a few other points. Then draw a smooth curve through the points.

  4. Using the graph, you can estimate that the number of incidents was about 125,000 during 2002 (t 6). EXAMPLE 4 Solve a multi-step problem STEP 3

  5. for Example 4 GUIDED PRACTICE 4.What If?In Example 4, estimate the year in which there were about 250,000 computer security incidents. SOLUTION 2003

  6. x 5.In the exponential growth model y = 527(1.39) , identify the initial amount,the growth factor, and the percent increase. for Example 4 GUIDED PRACTICE SOLUTION Initial amount: 527Growth factor 1.39Percent increase 39%

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