Can Lake Lanier sustain us? by Stephen

Can Lake Lanier sustain us? by Stephen - December 2016 Scholarship Essay

Water is to survival as math is to progress. When I was told by my calculus teacher that he invited the principal, teachers and members of the community to watch us present our project I was honored. Our teacher told us two weeks earlier that we needed to come up with a problem that affected either the world or community and solve it using calculus. A classmate and I wanted to do a project that involved our local area and interested us personally. Lake Lanier seemed like a perfect idea to work with since Georgia and Florida have been in ongoing legal battles for decades over the rights to the water in Lake Lanier. So, being able to calculate how much water in is in the lake and how long it could sustain a given population is a key element to any solution. We decided to calculate how long the water in Lake Lanier could sustain the population of Hall and Gwinnett County assuming normal water consumption including showering, drinking, and other normal activities.
The ultimate challenge was to determine the volume of Lake Lanier. We knew we couldn’t measure Lake Lanier as a whole since it has 692 miles of shoreline with varying depths. Therefore, we determined that we would measure the volume at sample locations. Equipped with a plan and process we went to my classmates dock in a relatively shallow cove. The first major task was to determine a process of collecting data by determining the size of the cove. Initially we decided to use his boat and a measuring tape to figure this out. I stood on the dock and firmly held the measuring tape as he headed into the cove with the end of the measuring tape tied to it. We quickly learned the measuring tape was too short as it broke and almost dragged me into the water. We had limited resources so we had to be creative. Using a lifejacket to mark the halfway point in the cove, we then measured 40 depths using the boat's depth finder. We collected data from multiple locations to provide a more accurate representation of the lake’s varied depths.
We had a full day on the lake collecting data, wakeboarding, and getting really sunburned. Now it was time to do the calculations to determine the volume of the lake. We did this by using the depths to find our quadratic regression line which gave us an equation that represented the bottom of the lake associated with the depths. We used this equation in our first integral which we then used in our double integral. We now had our first sample volume for the shallow area so we did the exact same thing for the deep area and averaged our two volumes. We knew our surface area in the sample areas so we then found the surface area of the whole lake calculated by the Corps of Engineers. Then we made a proportion using the surface areas and volumes and found the total lake volume. We divided the volume found by the water consumption of the two counties which we found by multiplying average water consumption per person per day by the overall population. With all the calculations completed, we finally had our answer. Lake Lanier could sustain Hall and Gwinnett county for 3,925 days.
The final step was to create a compelling video that highlighted all facets of the project. The water wars between the states may go on for many more years, but this project gave me insight into the importance of math in nature, science and the vital decisions of policy makers. I am motivated and excited to be a part of the fast paced progress being made in the areas of engineering, technology and science.