You have a secret that you to one person every hour each of the people that know the secret tells one person. The number of people who know when is N and T is the number of hours since you told the first person. Is an a linear function s of t?

Let's examine the function:

Before you tell anybody, only one person knows the secret (that is you), therefore: N (0) = 1

When the first person know, now two people know, therefore: N (1) = 2

After an hour, each of you would have told another person. So now, four people know, therefore, N (2) = 4

This pattern continues with the same manner where it doubles every hour.

As you can see, this is NOT a linear function. It is an exponential function where N (t) = 2^t