A biologist tracks a frog population that grows by 12% annually, but 15 frogs are lost each year to predation. Starting with 250 frogs, what is the population after 2 years?

Tue, 05 May 2026 17:21:52 +0000

**Why Are Frog Populations Changing, and What counts as Sustainable Growth?**
In recent years, scientists and nature enthusiasts alike have closely studied how amphibian populations respond to environmental pressures—especially the delicate balance between natural growth and external losses. Among the most monitored species are frogs, whose populations often shift due to a combination of reproduction rates and predation. One real-world example reveals a dynamic: starting with 250 frogs, the population increases by 12% each year, but 15 individuals are lost annually to natural predators. This pattern—growth tempered by consistent loss—raises an important question: how do these numbers translate over time? Understanding such population trajectories offers insight into broader ecological monitoring, especially as biodiversity faces growing challenges across the U.S. **Why Tracking Frog Populations Matters Now**
The study of frog populations reflects a broader trend in environmental tracking, where precise, data-driven analysis supports conservation planning and public awareness. With increasing attention on amphibian declines—a phenomenon linked to habitat loss, climate change, and invasive species—accurate population models become essential. A biologist tracking a frog population growing by 12% annually while losing 15 frogs yearly illustrates a key ecological principle: growth does not equal stability. Real-world monitoring reveals that sustained declines often occur even with moderate reproduction rates when predation and human impacts remain unmanaged. This dynamic is driving interest from researchers, educators, and concerned community members focused on ecosystem health. **How a Populations Model Actually Works with Real Numbers**
Calculating the population after two years involves a precise combination of percentage growth and fixed loss. Starting with 250 frogs:
- After Year 1: Growth of 12% yields 250 × 1.12 = 280 frogs. Subtract 15 lost to predation: 280 – 15 = 265 frogs.
- After Year 2: Growth on 265 frogs gives 265 × 1.12 = 296.8, which rounds to 297 frogs. Subtracting another 15 losses results in 297 – 15 = 282 frogs. This step-by-step approach demonstrates how small introductory gains are subtracted through predation, creating a realistic yet hopeful trend: continued growth despite unavoidable losses.