The salmon in Steelfin Lake decrease their numbers by approximately 20% each year. To counteract this,...

 

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The salmon in Steelfin Lake decrease their numbers by approximately 20% each year. To counteract this, the Steelfin Lake Conservation Society adds s salmon to the lake at the end of each year. Assume the starting population is 500 salmon, let s be the population of salmon after t years. Set up and describe a recursive model involving st, and use this to derive an explicit model relating st directly to t and s. Use your model to determine the minimum amount of salmon that need to be added to the lake each year in order to ensure the population of salmon in the lake will be at least 250 in any given year. The salmon in Steelfin Lake decrease their numbers by approximately 20% each year. To counteract this, the Steelfin Lake Conservation Society adds s salmon to the lake at the end of each year. Assume the starting population is 500 salmon, let s be the population of salmon after t years. Set up and describe a recursive model involving st, and use this to derive an explicit model relating st directly to t and s. Use your model to determine the minimum amount of salmon that need to be added to the lake each year in order to ensure the population of salmon in the lake will be at least 250 in any given year.