An ichthyologist observes that a certain fish population in the Great Barrier Reef declines exponentially, with a decay rate of 12% per year. What is the approximate population after 5 years if the initial count is 12,500?

Sun, 03 May 2026 14:39:14 +0000

**1. The Quiet Shift Beneath the Waves—Why Fish Populations Matter Now**
Coral reefs around the world are more than marine wonderlands—they’re vital indicators of ocean health. In recent years, climate stress and shifting ecosystems have intensified focus on species survival, with scientists closely tracking population trends. The decline of key reef fish populations in the Great Barrier Reef has gained attention due to visible changes in biodiversity and habitat quality. For U.S. audiences engaged with environmental science and conservation trends, this pattern underscores the broader impact of warming oceans and human activity. Understanding how these shifts unfold helps inform both public awareness and policy dialogue. **2. The Science behind the Decline: Why a 12% Annual Drop?**
Managed reef systems show clear signals of ecological imbalance, with key species like parrotfish experiencing exponential decline. A consistent 12% annual reduction reflects a combination of coral loss, rising sea temperatures, and pressure from overfishing—factors widely documented by ocean researchers. While not a straight linear drop, models using exponential decay accurately reflect this fading trend when averaged yearly. This pattern highlights the accelerating vulnerability of reef ecosystems under current environmental stressors. For American readers tracking marine conservation, such data fuels deeper inquiry into why these numbers matter beyond the reef itself. **3. The Math Behind the Drop: What’s the Population After 5 Years?**
To estimate the remaining fish population after five years with an annual 12% decay, exponential decay models apply. Starting with 12,500 fish, each year retains 88% of the prior count:
Year 0: 12,500
Year 1: 12,500 × 0.88 = 11,000
Year 2: 11,000 × 0.88 = 9,680
Year 3: 9,680 × 0.88 ≈ 8,506
Year 4: 8,506 × 0.88 ≈ 7,465
Year 5