Question: A marine biologist models the depth of a tide pool as $ d(t) = 10 + 4\sin\left(\frac{\pi t}{12}\right) $. What is the maximum depth?

["Understanding Tide Pool Depth: A Marine Biologist’s Insight", "Marine biology not only reveals the secrets of ocean life but also helps us understand the dynamic environments where aquatic species thrive—such as tide pools. For marine biologists modeling tidal patterns, precise depth measurements are crucial for assessing habitat conditions and protecting delicate ecosystems.", "A key example involves modeling the depth of a tide pool using the function:\n$$\nd(t) = 10 + 4\sin\left(\frac{\pi t}{12}\right)\n$$\nwhere $ d(t) $ represents depth in meters and $ t $ is time in hours.", "### What Does This Equation Mean?", "This model captures the rhythmic rise and fall of water levels caused by tidal forces. The sine function reflects natural periodic changes:\n- The amplitude of 4 meters indicates the maximum deviation from the average depth.\n- The vertical shift of 10 meters sets the average water level.\n- The period corresponds to a 24-hour cycle, matching typical daily tides.", "### What Is the Maximum Depth?", "To find the maximum depth, analyze the sinusoidal expression:\n$$\nd(t) = 10 + 4\sin\left(\frac{\pi t}{12}\right)\n$$\nSince the sine function oscillates between $-1$ and $1$, the maximum value of $ \sin\left(\frac{\pi t}{12}\right) $ is $1$. Substituting:\n$$\nd_{\ ext{max}} = 10 + 4(1) = 14\n$$", "Thus, the maximum depth of the tide pool is 14 meters.", "### Why This Matters for Marine Biological Research", "Accurate modeling of tidal depth helps scientists predict habitat conditions for intertidal species—from barnacles to algae—that depend on stable moisture and water coverage. Understanding maxima and minimums supports conservation strategies and ecosystem monitoring.", "By blending mathematical precision with biological insight, marine biologists provide vital data for preserving these vital coastal environments.", "---", "Key Takeaway:\nThe marine biologist’s model $ d(t) = 10 + 4\sin\left(\frac{\pi t}{12}\right) $ reveals that tide pool depth ranges from 6 meters (10 – 4) to 14 meters (10 + 4). This maximum depth of 14 meters highlights the dynamic nature of tidal habitats and reinforces the importance of such models in marine research and conservation.", "Keywords: tide pool depth, marine biology, sine wave model, tidal patterns, marine habitat, maximum depth calculation, oceanographic modeling, tidal cycle, intertidal zone research."]