Look through the fully worked out problem here:

Located on the Great Lakes system, American Falls, NY, is known for its stunning proximity to Niagara Falls and serves as a key part of the hydrological journey between Lake Erie and Lake Ontario.

While the Great Lakes are often associated with fresh water, seasonal changes, and diverse aquatic life, it’s intriguing to think about how modern technology and advanced mathematical models can assess the presence and movement of marine species, like sharks, in this unique environment.

Despite being a freshwater location, various waterways connected to the Great Lakes and surrounding areas experience the occasional movement of sharks and other migratory species. Advanced predictive modeling techniques allow researchers to monitor such occurrences with greater accuracy.

Our analysis leverages real-time environmental data—such as water temperature and tide levels—to predict shark density near American Falls on a specific date. This approach combines calculus-based models with observed environmental variables to give a detailed picture of shark presence across significant water expanses.

Let’s dive into the data for November 5, 2024, and explore how temperature and water level fluctuations impact the calculated shark density in this remarkable location.

Using the observed data for November and a temperature assumption based on seasonal averages, we can determine the likelihood of shark presence in this freshwater system. The key data include:

• Water Levels: Maximum at 559.90 ft, minimum at 558.37 ft, with a mean level of 559.25 ft.
• Temperature: Estimated at 10°C for early November.
• Calculation Method: Using a density function derived from temperature, we find an estimated shark density and apply it to the 641.4 km² area of water near American Falls.

Based on our calculations, we predict an approximate presence of 12,828 sharks in the area on November 5, 2024. This model gives us insight into the possible density of sharks and the role that seasonal changes play in influencing migratory patterns in even the most unexpected of locations.