Info about my design process is posted as an Instructable! Check it out!
https://www.instructables.com/Variable-Timer-Using-a-Potentiometer/
UPDATE: With the money I won from this project, I was able to buy more electronic components, thus allowing me to make a better prototype for this variable timer. I used a lot of the same components but changed the microcontroller from an Arduino Uno to an Arduino Nano. The Nano does the same thing except that it doesn't have as many ports as the Uno and there are no direct connections. I wish I had watched a video on how to solder to perforated circuit boards because as you can see, it looks horrible on the back. I was so surprised when it worked, but I am unsure how it will perform in the long run. As predicted, the connections are much stronger when soldered, so the timer worked wonderfully. I hope to tweak the code in the future and maybe make a completely different program that utilizes the components that are already on the board(perhaps a game?)