What If?
Find out what happens when the assumptions
change.
There are three key factors in this problem - the
initial population, the annual restocking amount,
and the annual population decrease rate.
1. Consider the three questions below. Make conjectures
for the answers.
- (a) If the initial population doubles, what
will happen to the long-term population?
(b) If the annual restocking amount doubles, what
will happen to the long-term population?
(c) If the annual population decrease rate doubles,
what will happen to the long-term population?
2. Enter new values in the spreadsheet and press
"Calculate" to generate new spreadsheet
outputs. Use the spreadsheet to answer questions
a, b, and c above, and compare the answers to your
conjectures. Any surprises? Any patterns? (Note
that Growth Factor = 1 - annual population
decrease rate)
3. Systematically investigate the effect that other
changes in these three factors will have on the
long-term population. Keep track of the results
of your investigations. Describe any patterns you
see.
4. Suppose the annual decrease rate
is 20% and the initial population is 3000, as in
the original situation. But now suppose you want
to change the restocking amount so that the long-term
population will be 7500. What restocking amount
should you use?
|
