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7.2 Exponential Patterns

7.2 Exponential Patterns
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  • 15. Trout Population

    A lake is stocked with 200 trout. The graph shows the growth of the trout population. What is the maximum sustainable population? Explain your reasoning. (See Example 5.)

    • Worked-Out Solution

      From the graph, the maximum sustainable population appears to be around 4000 trout.

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      _____      ___      ____       ___      ______  
     /  ___||   / _ \\   |  _ \\    / _ \\   /_   _// 
    | // __    | / \ ||  | |_| ||  / //\ \\  `-| |,-  
    | \\_\ ||  | \_/ ||  | .  //  |  ___  ||   | ||   
     \____//    \___//   |_|\_\\  |_||  |_||   |_||   
      `---`     `---`    `-` --`  `-`   `-`    `-`'   
                                                      
    
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  • 16. Trout Population Growth

    A lake is stocked with 200 trout. The graph shows the growth of the trout population. Make a table that shows the change in the number of trout for each year. Discuss any trends. (See Example 5.)

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     _____      ______   __   __    _____    _    _   
    |  __ \\   /_   _//  \ \\/ //  |  ___|| | || | || 
    | |  \ ||   -| ||-    \   //   | ||__   | || | || 
    | |__/ ||   _| ||_    / . \\   | ||__   | \\_/ || 
    |_____//   /_____//  /_//\_\\  |_____||  \____//  
     -----`    `-----`   `-`  --`  `-----`    `---`   
                                                      
    
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  • 17. Changes in Trout Population

    A lake is stocked with 200 trout. The graph shows the growth of the trout population. Make a table that shows the percent change in the number of trout for each year. Discuss any trends. (See Example 5.)

    data folder

    • Worked-Out Solution

      Begin by entering the data into a spreadsheet. Then, find the percent change each year.

      data folder

      The percent of increase is decreasing each year. Eventually, the percent increase will approach 0 and the population will stabilize.

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      _____     _____     ______     ___     _____    
     /  ___||  |  ___||  /_   _//   / _ \\  |  __ \\  
    | // __    | ||__      | ||    | / \ || | |  \ || 
    | \\_\ ||  | ||__     _| ||    | \_/ || | |__/ || 
     \____//   |_____||  /__//      \___//  |_____//  
      `---`    `-----`   `--`       `---`    -----`   
                                                      
    
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  • 18. Comparing Growth Patterns

    A lake is stocked with 200 trout. The graph shows the growth of the trout population. Make a table comparing the number of trout for each year in the graph to the number of trout each year if the trout population grew exponentially by 60% each year. Why is exponential growth unrealistic in this situation? (See Example 5.)

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    __    __    ______   __   _    __   __    _____   
    \ \\ / //  /_   _// | || | ||  \ \\/ //  / ____|| 
     \ \/ //    -| ||-  | '--' ||   \ ` //  / //---`' 
      \  //     _| ||_  | .--. ||    | ||   \ \\___   
       \//     /_____// |_|| |_||    |_||    \_____|| 
        `      `-----`  `-`  `-`     `-`'     `----`  
                                                      
    
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  • 19. Competing Species

    The graphs show the growth of the populations of two competing species of fish when they are released into separate ponds and when they are released into the same pond. Assume all the ponds are the same size and have the same resources. Compare the growth of the populations of the two species when they are released into separate ponds. (See Example 6.)

    • Worked-Out Solution

      When released into separate ponds, both species of fish experience a logistic growth pattern.

      Species A levels off with a population of about 1400 fish.

      Species B levels off with a population of about 1000 fish.

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      _____     ______    ______   _    _     ______  
     |__  //   /_   _//  /_____// | || | ||  /_   _// 
       / //     -| ||-   `____ `  | || | ||    | ||   
      / //__    _| ||_   /___//   | \\_/ ||   _| ||   
     /_____||  /_____//  `__ `     \____//   /__//    
     `-----`   `-----`   /_//       `---`    `--`     
                         `-`                          
    
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  • 20. Competing Species

    The graphs show the growth of the populations of two competing species of fish when they are released into separate ponds and when they are released into the same pond. Assume all the ponds are the same size and have the same resources. Compare the growth of the populations of the two species when they are released into the same pond. (See Example 6.)

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      ______    ______  __    __   __   __    _  _   
     /_   _//  /_   _// \ \\ / //  \ \\/ //  | \| || 
     `-| |,-    -| ||-   \ \/ //    \ ` //   |  ' || 
       | ||     _| ||_    \  //      | ||    | .  || 
       |_||    /_____//    \//       |_||    |_|\_|| 
       `-`'    `-----`      `        `-`'    `-` -`  
                                                     
    
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    Guest   10 months ago |
    Suck My dick is the answer
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