This calculator will determine the long-term population of a trout pond based on three initial conditions.

Enter values as follows:

• Initial Population: A value between 0 and 100,000.
• Restock Amount: A value between 0 and 100,000.
• Growth Factor: A value between 0 and 1. (Note that this assumes that the population will always stay the same or decrease without restocking.)

Press the Calculate button to generate a table of values showing the year (n) and the population (A(n).

The initial values for this applet (Initial Population = 3000, Restock Amount = 1000, Growth Factor = 0.8) can be used to investigate the following situation:

• There are currently 3000 trout in a pond.
• Due to fishing, natural death, and other causes, the population decreases by 20% each year, regardless of restocking.
• At the end of each year, 1000 trout are added to the pond.

How do the initial values relate to the numbers in the problem above?

Hold two of the three values constant, and repeatedly change the other value. (For instance, set Restock Amount to 1000 and Growth Rate to 0.5, but then enter values of 10, 500, 3000, and 25,000 for Initial Population. This will allow you to investigate the effect of Initial Population.) Try this for each of the three variables in the problem. What effect do each of them have on the situation?

Enter values for Initial Population and Restock Amount, and change Growth Factor to 1.

• What pattern occurs for the population when you press Calculate?
• What type of function do the numbers represent when Growth Factor = 1?