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4.1 Exponential Growth

4.1 Exponential Growth
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  • 7. Swine Flu Pandemic

    A pandemic is an outbreak of infectious disease or condition that spreads through a large part of the human population. There have been numerous pandemics throughout history such as smallpox and tuberculosis. Current pandemics include HIV and certain strains of influenza. Once a pandemic reaches Phase 6, the number of infected people can grow exponentially.

    From June 2009 through August 2010, the swine flu (H1N1) was considered a pandemic by the World Health Organization. Ten people in a community are infected with the swine flu. The next day, 26 people are infected. The growth rate is 160% per day. At this rate, how many people will be infected in 1 week? Graph the results. (See Example 3 and Example 4.)

    • Worked-Out Solution

      The formula for this exponential growth is

      The number of people who will be infected in 1 week is

      You can use a spreadsheet to graph the pandemic.

      data folder spreadsheet image

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     __   _     ______    _  _    __   __    _  _   
    | || | ||  /_   _//  | \| ||  \ \\/ //  | \| || 
    | '--' ||   -| ||-   |  ' ||   \ ` //   |  ' || 
    | .--. ||   _| ||_   | .  ||    | ||    | .  || 
    |_|| |_||  /_____//  |_|\_||    |_||    |_|\_|| 
    `-`  `-`   `-----`   `-` -`     `-`'    `-` -`  
                                                    
    
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  • 8. Exponential Growth of Pandemic

    Use the rate in Exercise 7 to find the number of people who will be infected after 1 week when the initial number of people infected is 50. (See Example 3 and Example 4.)

    A spreadsheet is available to help you complete this exercise.

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     _    _    _    _     _____     ______    ____    
    | |  | || | || | ||  /  ___||  /_   _//  |  _ \\  
    | |/\| || | || | || | // __     -| ||-   | |_| || 
    |  /\  || | \\_/ || | \\_\ ||   _| ||_   | .  //  
    |_// \_||  \____//   \____//   /_____//  |_|\_\\  
    `-`   `-`   `---`     `---`    `-----`   `-` --`  
                                                      
    
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  • 9. 1918-1920 Pandemic

    The 1918-1920 flu pandemic, commonly known as the Spanish flu, killed about 40 million people worldwide. That is more than twice the number of lives claimed by World War I. Estimates for the growth rate vary. Suppose 2 people are infected and the number of infected people triples every 3 days. How many people will be infected in 21 days? Graph the results. (See Example 3 and Example 4.)

    • Worked-Out Solution

      The formula for this exponential growth is

      Notice that if the number triples each day, this is a growth rate of 200%.

      The number of people who will be infected in 21 days is

      You can use a spreadsheet to graph the pandemic.

      data

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     _    _      ___     __   _      ___      ______  
    | |  | ||   / _ \\  | || | ||   / _ \\   /_   _// 
    | |/\| ||  / //\ \\ | '--' ||  / //\ \\    | ||   
    |  /\  || |  ___  ||| .--. || |  ___  ||  _| ||   
    |_// \_|| |_||  |_|||_|| |_|| |_||  |_|| /__//    
    `-`   `-` `-`   `-` `-`  `-`  `-`   `-`  `--`     
                                                      
    
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  • 10. 1918-1920 Pandemic

    Use the rate in Exercise 9. How many people will be infected in 42 days? (See Example 3 and Example 4.)

    A spreadsheet is available to help you complete this exercise.

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      _  _     _____    _    _     _____      _____  
     | \| ||  |  ___|| | || | ||  |  ___||   / ___// 
     |  ' ||  | ||__   | || | ||  | ||__     \___ \\ 
     | .  ||  | ||__   | \\_/ ||  | ||__     /    // 
     |_|\_||  |_____||  \____//   |_____||  /____//  
     `-` -`   `-----`    `---`    `-----`  `-----`   
                                                     
    
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  • 11. Exponential Graph

    Describe the graph of an exponential growth model. (See Example 3 and Example 4.)

    • Worked-Out Solution

      The graph of the exponential model is a curve that rises more and more rapidly as n increases.

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      _____     _____     _____      ___              
     |__  //   |  ___||  /  ___||   / _ \\      ___   
       / //    | ||__   | // __    / //\ \\    /   || 
      / //__   | ||__   | \\_\ || |  ___  ||  | [] || 
     /_____||  |_____||  \____//  |_||  |_||   \__ || 
     `-----`   `-----`    `---`   `-`   `-`     -|_|| 
                                                 `-`  
    
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  • 12. Growth Rate

    Many factors affect the spread of a disease. Describe some factors that would influence the growth rate of an infectious disease. Would these factors increase or decrease the growth rate?

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       _____     ___      ____      _____     _____   
      / ___//   / _ \\   |  _ \\   |  ___||  |__  //  
      \___ \\  / //\ \\  | |_| ||  | ||__      / //   
      /    // |  ___  || | .  //   | ||__     / //__  
     /____//  |_||  |_|| |_|\_\\   |_____||  /_____|| 
    `-----`   `-`   `-`  `-` --`   `-----`   `-----`  
                                                      
    
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