Chapter 11.5, Problem 45PPS

To determine

Find the population of the lake converges to any particular value. If not, explain.

Answer to Problem 45PPS

No; the population of fish will reach 12,500.

Explanation of Solution

Given:

Suppose a lake is populated with 10,000 fish. A year later, 80% of the fish have died or been caught, and the lake is replenishes with 10,000 new fish. If the pattern continues, will the lake eventually run out of fish ? If not, will the population of the lake converge to any parlier value? Explain.

Concept Used:

No; the population of fish will reach 12,500.

Each year, $20\%\text{of}12,500\text{or}2500$ fish, plus 10,000 additional fish, yields 12,500 fish.

Thus, no, the population of fish will reach 12,500.