The graph shows that selection sort is quadratic, which is all we usually
need to know.

But sometimes you want to get a proper numerical result: If I use that
program on the same computer under the same circumstances, how long will
it take to sort an array of N strings?

We know that the formula

         time = k * (size squared)

is as accurate as is practically possible, but what is the value of K?

With a big enough piece of graph paper, we could just extend the line and
see what the value of time is when it reaches back to size=1, but we haven't
got a big enough piece of graph paper.

Just from one of our observed timings, we can substitute it into the
formula and calculate K.

it took 0.026147 seconds to sort 1000 things.

so 0.26 seconds = k * 1000 * 1000

which means that the constant k = 0.26 micro-seconds, or 2.6e-7 seconds.

To sort a mere million items it would take about 260,000 seconds, which is
just over 3 days.

To sort a billion things it would take over 8,000 years.

When an algorithm is quadratic, doubling the amount of data quadruples the
time, ten times more data takes a hundred times as long, a thousand times
more data takes a million times as long.