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4.1 Exponential Growth

4.1 Exponential Growth
  • Math Help

    To use a spreadsheet to make a column graph similar to the one in Example 3, use the following steps. [Note that Step 6 uses the exponential growth formula given in Example 3, .]

    1. Enter the titles "Week, n" and "Number of Mice" into Row 1.
    2. Enter 0 into cell A2.
    3. Enter the formula =A2 + 1 into cell A3.
    4. Select cell A3. From the Edit menu, choose Copy.
    5. Select cells A4 through A44. From the Edit menu, choose Paste.
    6. Enter the formula = 2*(1 + 0.3)^A2 into cell B2.
    7. Select cell B2. From the Edit menu, choose Copy.
    8. Select cells B3 through B44. From the Edit menu, choose Paste.
    9. Select cells in Rows 1-44, Columns A and B.
    10. From the Insert menu, choose Chart….
    11. In the Chart Wizard, select Column from the Chart type: list. Then click Next.
    12. Select the Series tab.
    13. From the Series list, select "Week, n." Then click Remove.
    14. From the Series list, select "Number of mice." Enter =Sheet1!$A$2:$A$44 into Category (X) axis labels. Click Finish.
  • Consumer Suggestion

    Did you know mice eat between 15 and 20 times per day? To help keep mice out of your cupboards and your home, make sure food containers are sealed or closed tightly. Cupboard surfaces should be clean and dry. If you find a hole in your home's exterior, foundation, walls, or cupboards, fill it with steel wool. For more about maintaining a mouse-free house, visit The Family Handyman.

  • Checkpoint Solution

    Instead of one breeding pair (2 mice), there are 1000 breeding pairs (2000 mice) for the initial value. So the formula becomes

    So, 1000 breeding pairs and their offspring can produce about 122,081,763 mice in just 42 weeks.

    You can check this answer by downloading the spreadsheet and entering 2000 for the initial number of mice.

  • Comments (2)

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    system user
    Guest   1 decade ago |
    Here is a link to a horrible video about a mouse plague in Australia.
    system user
    Ron Larson (author)1 decade ago |
    Be sure that you see the basic characteristic of exponential growth. For each successive period of time, the population grows by the same percent. For instance, a savings account represents exponential growth because the balance in the account increases by 3% (or whatever the rate is) each year.