An estate manager is responsible for stocking a small lake with fish. He begins by introducing 1000 fish.
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Suppose that every year, only 10% of the fish in a lake have surviving offspring. If there were 100 fish in the lake last year, there would now be 110 fish. If there were 1000 fish in the lake last year, there would now be 1100 fish. Absent any inhibiting factors, populations of people and animals tend to grow by a percent of the existing population each year.
Suppose our lake began with 1000 fish, and 10% of the fish have surviving offspring each year. Since we start with 1000 fish, P0 = 1000. How do we calculate P1? The new population will be the old population, plus an additional 10%. Symbolically:
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