An entomologist observes that a termite colony grows by a factor of 2.5 every 6 months. Starting with 80 termites, how many are there after 18 months?

["How Termite Colonies Expand: A 2.5× Growth Rate Over 18 Months (Starting 80 Termites)", "Understanding how insect populations evolve is crucial in entomology, pest management, and ecological studies. One fascinating example comes from long-term observation of termite colonies, where growth rates often follow exponential patterns. This article explores how an entomologist’s data—showing a colony doubling (but faster) by a factor of 2.5 every 6 months—leads to explosive population growth over time. We’ll calculate the termite colony size after 18 months, beginning from just 80 individuals.", "### The Biology Behind Rapid Termite Growth", "Termites are eusocial insects with highly organized colonies that reproduce rapidly under favorable conditions. Unlike simple doubling, many termite colonies grow by increasingly complex developmental stages—workers, soldiers, reproductives—leading to accelerated increases. The observed growth factor of 2.5 times every 6 months reflects this biological reality, where successive generations or synchronized reproduction phases trigger exponential scaling.", "This kind of growth pattern follows the formula for exponential growth:", "[\nN(t) = N_0 \ imes r^t\n]", "Where:\n- (N(t)) = population after time (t)\n- (N_0) = initial population = 80 termites\n- (r) = growth factor per cycle = 2.5\n- (t) = number of 6-month periods", "### Calculating Population After 18 Months", "Since 18 months equals three 6-month intervals, we set (t = 3). Applying the formula:", "[\nN(3) = 80 \ imes 2.5^3\n]", "Now compute (2.5^3):\n[\n2.5^3 = 2.5 \ imes 2.5 \ imes 2.5 = 6.25 \ imes 2.5 = 15.625\n]", "Then multiply by the starting population:\n[\nN(3) = 80 \ imes 15.625 = 1250\n]", "### Population Over Time: A Timeline of Growth", "- 0 months (Start): 80 termites\n- 6 months: (80 \ imes 2.5 = 200) termites\n- 12 months: (200 \ imes 2.5 = 500) termites (or (80 \ imes 2.5^2 = 80 \ imes 6.25 = 500))\n- 18 months: (500 \ imes 2.5 = 1250) termites (or (80 \ imes 2.5^3 = 1250))", "### Why This Growth Matters", "From an entomological perspective, such rapid termite expansion underscores why early detection and control are essential. A small colony of 80 termites—easily concealed in wood or soil—can grow to over 1,200 individuals in just 18 months. This exponential increase explains why biological surveys and population modeling are vital in preventing structural damage and ecological disruption.", "### Key Takeaways", "- A termite colony growing at 2.5× every 6 months expands dramatically over time.\n- Starting with 80 termites, the population reaches 1,250 after 18 months.\n- Understanding these growth rates enables better pest control strategies and ecological forecasting.\n- Exponential growth patterns in insects highlight the importance of early intervention.", "### Final Answer\nAfter 18 months, a termite colony starting with 80 individuals grows to 1,250 termites with a growth factor of 2.5 every 6 months.", "---", "By recognizing these patterns, entomologists and pest management professionals can predict population trends, implement timely control measures, and protect buildings and ecosystems from termite devastation. The rapid rise from 80 to 1,250 termites in 18 months is a powerful example of exponential growth in nature—driven by the survival and reproduction genius of these small but formidable insects."]