Course: Precalculus, MATH-130
Professor: Janice Stencil
Assignment Title: Salinity
For this assignment I was tasked with determining a quadratic, cubic, exponential, and sinusoidal model for the salinity of the Chesapeake Bay. Salinity is the concentration of salt in a body of water and is typically measured in parts per thousand (abbreviated ppt). I was given three values for the salinity at three different points in time, which are provided in the table below. Using this information, I was able to make an equation for each mathematical model.
For each model, I started with the general form of the function and substituted the given information into the equation. The general form of each model where S is equal to salinity and t is equal to time is as follows:
Quadratic: S(t) = at2+bt+c
Cubic: S(t) = at3+bt2+ct+d
Exponential: S(t) = aebt+c
Sinusoidal: S(t) = acos(bt)+d
Once I solved for the unknown variables, I had an equation that I could use to predict future values for salinity and make a graph to visualize the data.
I am interested in pursuing a STEM based major. This assignment provided me with the opportunity to calculate several equations, interpret data, and graph my results. These skills will serve as a solid foundation as I continue to build upon them in calculus this semester. The process used to solve equations and make conclusions in this assignment will be necessary as I encounter similar problems in mathematics.
Another skill I developed while completing this assignment was the ability to effectively communicate mathematical analysis in a formal report. I can apply this knowledge when I take chemistry or other lab sciences in the future. The ability to present data in a logical and understandable way will be necessary as I complete other assignments in my classes.
The final part of this assignment gave the actual value for salinity on the third year, which was 5.9 ppt. According to this new information, I was able to determine that Equation A of the sinusoidal model was the most accurate.
Prediction on the third year: 16 ppt.
Graph: Parabola- increasing to a point and then decreasing indefinitely
Equation A: S(t)=-3t3+7t2+4t+4
Prediction on the third year: -2 ppt.
Graph: Decreases quickly over time
Equation B: S(t)=t3-5t2+12t+4
Prediction on the third year: 22 ppt.
Graph: Increases quickly over time
Prediction on the third year: 18 ppt.
Graph: Increases infinitely but never reaches 20 ppt.
Equation A: S(t)=-32/5cos(1.823t)+52/5
Prediction on the third year: 6 ppt.
Graph: Fluctuates direction periodically
Equation B: S(t)=-32/5cos(4.459t)+52/5
Prediction on the third year: 6 ppt.
Graph: Fluctuates direction frequently
Challenges and Successes
A challenge I encountered while working on this assignment was the fact that it was exclusively online. As a result, there was less interaction with my professor. This made asking questions difficult as I would have to wait for a published office hour or a reply via email. Despite the challenge, Professor Stencil was interactive and quick to respond.
There were technical challenges with the visibility of the equations and values that I turned in. This provided additional stress as I had to figure out why the equations were not showing and how I could get my professor to see them. Thankfully, Professor Stencil and I were able to troubleshoot the issue and she was able to see my calculations.
The biggest challenge I faced was that I discovered an error in the assignment. The assignment indicated that there was only one correct graph for the sinusoidal model, but the answer I calculated indicated that there were two. I contacted Professor Stencil, and we were able to collaborate and agree that there were two correct graphs.