An ichthyologist tracks a fish population in the Great Barrier Reef. Initially, there are 1,200 fish. Over three years, the population grows at 8% annually, but each year, 4% of the population migrates to other reefs. What is the population after three years, compounded annually with growth then migration?

Wed, 22 Apr 2026 09:22:13 +0000

**An ichthyologist tracks a fish population in the Great Barrier Reef. Initially, there are 1,200 fish. Over three years, the population grows at 8% annually, but each year, 4% of the population migrates to other reefs. What is the population after three years, compounded annually with growth then migration?** In a climate where marine ecosystems face increasing pressure from warming oceans and human activity, a quiet yet compelling story unfolds in the waters of the Great Barrier Reef. Researchers are closely monitoring how fish populations evolve under natural and environmental influences—a field where long-term data reveals critical insights. One dynamic example involves a population starting at 1,200 fish, growing steadily at 8% each year, yet losing 4% annually to migration. Understanding this pattern helps scientists anticipate broader ecological shifts and supports conservation efforts across increasing global interest in reef health. Now, focusing specifically on the compound growth and migration scenario, what does the math look like? When fish populations grow by 8% annually, they multiply by 1.08 each year. But competition for space and gradual reef shifts result in 4% leaving the area each year—meaning only 96% of the population remains at year’s end. This isn’t simple subtraction but a compounded process where growth and loss unfold sequentially: first expand, then apply loss to the larger base. Let’s explore how this plays out year by year: