Equal steps and doubling

Suppose a clinic adds ten appointments every week. After ten weeks, it has added one hundred appointments. Next week adds another ten. This is linear growth: the amount changes by the same fixed step each time.

Now start with one appointment and double the total every week. The sequence is 1, 2, 4, 8, 16. After ten weeks, the total is 1,024. This is exponential growth: each new value is a multiple of the one before it.

At first, the doubling series looks less important than the steady increase. For several weeks, adding ten still produces the larger total. Then the doubled series catches up and passes it. The rule never changed; only the scale did.

That distinction matters whenever people plan from a small early number. A quiet week may mean that nothing unusual is happening. It may also be the early stage of a process that is growing much faster than it appears.

The next question is why this pattern is so easy to miss in ordinary life.