Hey! Our dog-tors wanted to experiment a little before the new year. Since we were able to collect all the data last time, Dr. Eyelovedogs and Melovecats thought it would be a good idea to do so again!
And before you start thinking, "Are you going to use actual animals?" the answer is - well, yes! However, Dr. Melovecats proposed a psychological experiment that involves music, and nothing physical. In this experiment, you and I will record the effects it has by measuring my most amazing, nice, loving best friend's cat's (Teddy) serotonin levels.
We have our main equation, but let's also find our solution. I'll go ahead and write this down really quick!
We can further simplify this by assuming Teddy wasn't receiving any serotonin before listening to music (poor Teddy). This means we plug in 0 for our y and t values to find C, which is -250. That said, this equation we found should give us more exact serotonin values, in comparison to the other equation (Euler's Method).
Making a Code
In order to better get an understanding for this graph, let's go ahead and create a code to form a graph for us.
This graph plots our two equations, both Euler's Method and the solution equation. This begins to show a graph that begins to level out and reach an equilibrium.
Results
Teddy seems to like music but only for a certain amount of time before his serotonin levels begin to level out, as seen with Euler's Method - which is an approximation.
That said, as step sizes get smaller and smaller, the plots will come closer to the solution line. In this case, step size 1 gave one of the best graphs, with step size 2 in second place (get it?).
Although step size 4 forms somewhat of a curve, it's hard to determine due to said large step size.
Let's go ahead and determine what the equilibrium is by equating the differential equation to 0.
To sum up, the equilibrium for how much serotonin Teddy will have listening to music will be 250ng - looks like music is pretty good for cats at least! Let's let Dr. Melovecats know!
Reflection
My time in calculus was very enjoyable and allowed me to learn about some stuff regarding my career path. Well, at least at the time – now I wanna be a music teacher, so I tried to incorporate that into my final milestone. But even if I did stick with vet studies, I don’t think I would change a thing. Staying in my hometown is like a dream to me – but maybe away from my parents so I can be somewhat independent.
Regardless if I become a veterinarian or a music teacher, I think one of the most important things the interviewing milestone taught me is just professionalism. It’s broad but the idea itself mostly tailors to proper clothing, manners, and so forth – almost like your necessities.
The stuff I learned in calculus has helped me really see that math is everywhere. I remember my pre-cal teacher in high school absolutely stressing this to us but I don’t know why I never really let it get to me. This project really helped me see that though, even if the scenarios weren’t real or absolute, because what really matters is that they are possible and could definitely happen. For example, a scholar could absolutely do an experiment regarding music and animals, which has already been done.
All-in-all, this project helped me better understand calculus but also its application into the real world, especially regarding medicine.