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