Question

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

Answer 1

No, it is not a linear function. It is an exponential function.

Explanation:

You have a secret that you tell to one person.

Every hour, each of the people that know the secret tells one person.

Let N be the people who know the secret.

Let t be the number of hours since you told the first person.

Now, when only you know the secret, means 1 person.

N(0) = 1

Next hour, there are now 2 people that know the secret.

N(1) = 2

After the next hour, these 2 people will tell 2 more people, so people doubled to 4.

N(2) = 4

One hour later it will be N(3) = 8

We can see the pattern as following.

`N(t)=2^(t)`

Therefore, the function is exponential not linear.