exponential growth project

Unit four project—bunny project (exponential growth)—50 points

We discussed earlier that exponential growth (doubling) cannot continue forever! Something will happen to cause the growth to stop. However, act as if growth can continue and consider the following scenario:

A rabbit matures at 6 months, has a gestation period of 30 days—call it one month (with a 4 week time lapse after birth to become fertile--again, call it one month), and has a litter of 10 rabbits (assume that half are female). Assuming perfect conditions exist and continue, how many rabbits are there in 2.5 years (30 months)? What is happening with the population of the rabbits?

Here is what you need to do. For a 30 month period:

· Track the number of baby bunnies the original pair of bunnies have. (how many?)

· Track the number of baby bunnies the original bunnies babies have. (how many?)

· Track the number of baby bunnies the baby bunnies babies have. (how many?)

· You get the idea…

· Month “0” begins with two mature bunnies that have already …

As part of your project…

· Use an excel spreadsheet to total number of baby bunnies over the 30 months.

· Track the growth bimonthly (create a table of the month –independent variable—and population—dependent variable).

· Use your calculator to find a regression line. Show the table (include data in your table for the first 30 months) that you use to determine the equation. Your table will need two lists (time and population) to be used for the regression function.

· Assume the growth was linear instead of exponential, what is the difference in the number of bunnies after three years (36 months)? Use your linear regression function to compare with the exponential function based on your list of data.

Make sure that you include:

1. Both names on your project and that you include a description and the percent of contribution for each member 5 points

2. A graphic tracking of the growth (visual display of growth) and a numeric tracking of growth--with bi-monthly tracking (use your excel sheet for this) 10 points

3. An approximation of the population over the 30 month period—from the Excel sheet

10 points

4. Determine an exponential regression equation from the table of data ( include data from 30 months) and project populations for 30 months and 60 months. 10 points

5. Use the linear regression formula to predict the population for 30 months and 60 month and compare this with the exponential equations. Discuss this. 10 points

6. A brief narrative summarizing important aspects of this project 5 points

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