Jon made a Facebook video

Question

Jon made a Facebook video. On the first day, 2 people watch it. On the 2nd day, each of those 2 people get 2 people to watch it. Assuming the pattern continues, answer each question.

1. Number of people day 1:____

2. Number of people day 2:____

3. Number of people day 3:____

4. Number of people day 4:____

5. Number of people day 5:____

Recursive Formula:

f(1) = ___

f(n) = ___

Explicit Formula: f(n) = ___

Answer 1

f(1) = 2. This means "The first term is two"

f(n) is calculated by taking the previous term (the one BEFORE f(n)), and multiplying by two.

f(n - 1) means "the term before the nth term"

This is how we write the recursive formula: f(n) = 2 * f(n - 1) This shows how to get the nth term if you know the term before it.

The Explicit formula shows that we are repeatedly multiplying by two, so we use an exponent. We don't need to know the term before, we see that the tenth term is two to the tenth power, the hundredth term is two to the hundredth power, etc.

The exponent matches the n.

f(n) = 2^n