Question

View the Table2. What expression can we write to find the number of possible outcomes for 7 coins?

Answer 1

Function Modeling

We use functions to model certain facts that occur in real-life events.

It's given a table where the number of possible outcomes when flipping a coin is a function of the number of coins flipped.

We can observe each file of the number of outcomes doubles the previous value, that is:

32 = 16*2

16 = 8*2

8 = 4*2

This suggests the relationship between n (the number of coins) and O (the number of outcomes) is exponential, i.e., the variable is an exponent, in fact, a power of 2:

`O(n)=2^n`

For n = 7 coins:

`\begin{gathered} O(7)=2^7 \\ O(7)=128 \end{gathered}`

There are 128 possible outcomes for 7 coins