Question

How many subscribers will the blog have 12 weeks after you created it

Answer 1

You know that the third week you have one subscriber, the fourth one you will have 4, the fifth you will have 16 and so on. This behavior can be modeled by an exponential function with base 4 (sinde the number quadruples each week), then we will have a function of the form:

`f(t)=a(4)^(t-b)`

where a is the initial number of subscribers and b is the number of week with the first subscriber. In this case a=1 and b=3, hence the function that gives us the number of subscribers is:

`f(t)=4^(t-3)`

Now that we have the function we plug the week we want, in this case 12, then we have:

`\begin{gathered} f(12)=4^(12-3) \\ f(12)=262144 \end{gathered}`

Therefore at the twelfth week the number of subscribers will be 262,144