Answer: it will take 7 years for the lake to have no more trout, considering the fishermen's impact and the natural population oscillation.
Explanation:
Let's analyze the problem step by step:
1. The average trout population is 20,000.
2. The population naturally oscillates above and below average by 2,000 every year. This means the population goes up by 2,000 and then goes down by 2,000, making it a net change of 0 in the population every two years.
3. Fishermen catch 3,000 fish every year.
We want to find out how long it will take for the lake to have no more trout. Since the fishermen are catching 3,000 fish per year and the natural population oscillation has a net change of 0 over a two-year period, the main factor affecting the trout population is the number of fish caught by fishermen.
Let's denote the number of years it takes for the lake to have no more trout as "x". We can represent this situation with the following equation:
20,000 - 3,000x = 0
Now we can solve for x:
3,000x = 20,000
x = 20,000 / 3,000
x ≈ 6.67
Since we cannot have a fraction of a year, we need to round up to the next whole number to ensure that there will be no more trout left in the lake.