Portfolio Type 2 Fish numbers

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We were first given the equation where is the growth factor and is the population at year. A logistic model is one that grows and then stabilizes over time. This will be shown in the following set of problems.

1. The biologist estimates that if 10,000 fish were introduced into a lake, then the population of the fishes would increase by 50% the first year but then level off and never exceed 60,000 fishes. Therefore we are given a set of initial and eventual numbers that we can assign variables to:

Thus we can fill the ordered pairsand these points are indicated on the graph below:

The window and table values for the graph above are:

The window of the graph shows the scale of the graph and the values give evidence for the points on the graph.

The slope of the line with coordinatesis:

Therefore

is the linear growth factor in terms of with a slope,

2. Since and we figured , we can derive:

.

3. In order to determine the fish population over the next 20 years,