To determine the number of triangles in any given level of the pyramid, we can use the formula:
f(l) = 3(l-1)^2 + 1
where l represents the level of the pyramid.
The formula can be derived by noticing that each level of the pyramid consists of a square with sides of length l-1, and four triangles attached to each side of the square. Each of these triangles has a base of length l-1 and a height of l-2. Therefore, the area of each triangle is (1/2)(l-1)(l-2), and the total area of the four triangles on each level is 2(l-1)(l-2). Adding this to the area of the square, which is (l-1)^2, gives the total number of toothpicks in the level: 3(l-1)^2. Finally, we add 1 to account for the top toothpick.
Thus, the function is:
f(l) = 3(l-1)^2 + 1