Projects - Cengage Learning

C-110 Appendix C
MINI PROJECT
Perspective and Alternative Scenarios for
Population Growth Models
As background for this mini project, someone in your group or in the class at
large should review and summarize Example 5 for everyone else.
1. Refer to Figure 2 on page 1002,* which shows a scatter plot for the size of
the rabbit population in Example 5* at the end of years t 0, 1,..., 5. In
the text it was mentioned that the picture suggests exponential growth.
Another possibility is quadratic growth. Explore this as follows. Using a
graphing utility, enter the six data points specified in Figure 2 and create a
scatter plot similar to the one shown in Figure 2. Then use the exponential
regression option on the graphing utility to find the exponential function
that best fits the data. Add the graph of the exponential function to your
scatter plot. Next, add a quadratic regression curve to the picture. Which
curve seems to fit the data points better?
2. In Example 5, suppose we make a change in the model so that the given
recursive sequence is
P 0 16
P t 0.0003P t1 (3000 P t1 ) (t 1)
Use a graphing utility to investigate the population trend or trends. On
paper, in complete sentences, compare and/or contrast your results with
those in Example 5.
3. In Example 5, instead of beginning with 16 rabbits, suppose that we start
with the much larger initial population size P 0 3200. (Assume, however,
that the recursion equation from Example 5 remains the same.) Use a
graphing utility to investigate the population trend or trends. On paper, in
complete sentences, compare and/or contrast your results with those in
Example 5.
4. (a) Follow Exercise 3, assuming that the size of the initial population is
P 0 6330. (Compare and/or contrast your results with those in Exercise
3, rather than Example 5.)
(b) Find out what happens if P 0 6334. In terms of the rabbit population,
can you suggest a possible interpretation of the results?
*Precalculus: A Problems-Oriented Approach, 7th edition