Limited Population Growth
Part 3:
Fruit Flies: A Numerical Example
We assume that our laboratory
population of fruit flies initially has 111 flies. We further assume
that the maximum population supported by the laboratory environment is
1000. In order to carry out our computations we also need a value
for the proportionality constant c: On the basis of (simulated)
experience with laboratory populations, we take c = .000098. We
will first predict our population every 5 days, i.e., Delta-t
= 5. Use your helper application to calculate the missing values for
the following table, using the formulas from Part 2. (The final row of
values is supplied so you can check your calculations.)
| Time t (days) |
Population P |
Slope = dP/dt |
| 0 |
P0 =
111 |
slope0 = ? |
| t1 =
? |
P1 =
? |
slope1 = ? |
| t2 =
? |
P2 =
? |
slope2 = ? |
| t3 =
15 |
P3 =
310.435 |
slope3 = 20.9784 |
It may seem strange to report
non-integer population values ("How can we have .435 of a fly?").
However, rounding these numbers during the computations can have undesired
consequences, so we retain the decimal values. Rounding to integer values
can always be done later.
In the next Part we automate
this process so you don't have to do it step by step.
Send comments to the
authors <modules at math.duke.edu>
Last modified: September
20, 1997
