Question

I am doing the 100 meter men's freestyle swimming lab (in case you know what I am referring to) and I need to fibd the lower limit analytically.
I am given a table of data containing the years after 1900 and the time in second of each country , for example:
Time. Country.
55.4 seconds. Australia

Year after 1900
56

And I first thought I would just set a limit, with something like , lim f(x)
X--》0
But my teacher said it couldn't be zero.
Plz help!!!

Answer 1

well lets think it might be like a hot stone cooling down to some room temperature Tf

Google Newton's law of cooling

T = Ts +(To-Ts)e^-(k t)

To is your original 1900 time
Ts is your final time in 2100 or whatever which is the fastest one can ever go
k is a constant that kind of fits your data points.
You can fool around with the values of k and how long it takes to reach the final record time Ts
to get a good fit with your data