Answer:
The explicit equation is:
[tex]\begin{gathered} f(x)=4^x \\ \\ \text{For x = 0,1,2} \end{gathered}[/tex]
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
[tex]y=4^x[/tex]
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
[tex]f(x)=4^x[/tex]
To check
For x = 0 (At the beginning)
[tex]f(0)=4^0=1\text{ dot}[/tex]
For x = 1 (Day One)
[tex]f(1)=4^1=4\text{ dots}[/tex]
For x = 2 (Day Two)
[tex]f(2)=4^2=16\text{ dots}[/tex]
