Functions and Activities

As I learned about functions in Math, I started to relate the activities I did with functions, although without definite accuracy. One activity stood out as I did it a lot: running. I noticed that when I ran, my heart rate would pick up, and my speed would increase as well as my displacement. My heart rate as a function can be shown as f(x)=x^2, as x(my speed), increases, y(my heart rate) increases too. My velocity as a function can be shown as f(x)=2x+t^2. With this formula, as my speed increases, my displacement also increases. Also, with this formula, with the t variable, the average and instantaneous rate of change can be found.