Answer:
f(n) = 3^(n -1)
Explanation:
You want a function that describes the relation shown in the table.
Analysis
The values under Steps are sequential, which makes determining the function a lot easier.
The values listed under Black Triangles don't have a common difference, but they do have a common ratio:
r = 3/1 = 9/3 = 27/9 = 3
Exponential function
For this function, we'll use 'n' as the independent variable (the number of steps), and we'll call the function 'f'.
For common ratio r and a pair of table values (n, f(n)) = (a, b), the exponential function can be written as ...
f(n) = b·r^(n -a)
With r=3 and (a, b) = (1, 1), this becomes ...
f(n) = 1·3^(n -1)
The multiplier 1 isn't really needed, so we can use ...
f(n) = 3^(n -1)