Question

I just need to make a explicit equation based to this

Answer 1

The explicit equation is:

`\begin{gathered} f(x)=4^x \\ \\ \text{For x = 0,1,2} \end{gathered}`

Step-by-step explanation:

At the beginning, there was only one dot

Day One has 4 dots, and Day Two has 16 dots

Notice that the increase is geometric.

1 to 4 to 16

The common ratio is 4, because 4/1 = 16/4 = 4

So, we have

`y=4^x`

Where y represents the number of dots, and x is the day number.

Let y = f(x), and we have the explicit equation we require

`f(x)=4^x`

To check

For x = 0 (At the beginning)

`f(0)=4^0=1\text{ dot}`

For x = 1 (Day One)

`f(1)=4^1=4\text{ dots}`

For x = 2 (Day Two)

`f(2)=4^2=16\text{ dots}`