Create a function that determinates how much a man walkes

Question

First, sorry for any grammar mistake... english isn't my native language.

So, i was solving these math problems when i faced with a question that seemed easy but when i started to solve it, I failed misarable. :(

The question says about this guy that start running 700 meters in 10 minutes and slow down in a rate of 20 meters every 10 minutes. So between 10-20min he runs 680m and so on. The question wnats me to create a function that gives how much he ran in a certain time 'x' (minutes). How do i do it?

Answer 1

There are two ways to do that. One is to create a "piecewise function": $d(t)= \left\{\begin{array}c 70t & t\le 10 \\ 700+ 2t & t> 10 \end{array}\right\}$

The other is to use the "Heaviside step function", H(x), which is defined as "H(x)= 0 if x is less than or equal to 0, 1 if x is larger than 0". $d(t)= 70t+ (700- 68t)H(t- 10)$. Of course that just "hides" the piecewise definition in the step function.