Fully worked out problem here:

Virginia Beach, with its scenic coastlines and bustling boardwalk, is a magnet for tourists and marine enthusiasts alike. While visitors flock to its shores for relaxation and recreation, just beneath the waves lies a dynamic ecosystem teeming with marine life, including various species of sharks.

Influenced by the Gulf Stream and the Chesapeake Bay, Virginia Beach provides a diverse habitat that attracts sharks such as sandbar and tiger sharks, who thrive in its temperate waters. As the seasons change, so do the behaviors of these marine predators, with migration patterns and feeding habits often driven by shifts in water temperature, ocean currents, and tidal flows.

Today, November 7, 2024, we’re taking a closer look at shark density in the waters surrounding Virginia Beach, utilizing a calculus-based model that incorporates environmental data to predict population concentrations.

At a water temperature of 65°F (18.3°C), which is within the typical range for early November, we see ideal conditions for monitoring shark movements. Tidal data shows high tides reaching 4.0 feet at 11:13 AM and 3.0 feet at 11:40 PM, with low tides at 4:47 AM and 5:53 PM, creating fluctuations that influence sharks' proximity to shore throughout the day.

Using a temperature-driven density model, our calculations suggest an estimated shark density of approximately 104 sharks per square kilometer. When applied to Virginia Beach’s 641.4 square kilometers of water, this equates to a projected presence of around 66,857 sharks in the area. This real-time prediction, grounded in calculus and empirical data, provides valuable insights for researchers, conservationists, and beachgoers alike, enhancing our understanding of shark movement patterns. By continuously refining these models with new data, we aim to make Virginia Beach’s waters safer and to foster greater respect and awareness for these vital ocean predators.