Question

A tree of height y meters has approximately B branches, where B = y − 2. Each branch has approximately n leaves where n = 9B2 − B. Find the approximate number of leaves of a tree as a function of height.

Approximate number of leaves of a tree

Answer 1

we are given an expression representing the number of branches in terms of the height of the tree, y: B = y − 2 and the number of leaves n = 9B2 − B. the function of the number of leaves as a function of height is

n = 9B^2 − B
n = 9(y-2) ^2 − (y-2)
n = 9* (y2-4y+4) -y +4
n = 9y2-36y+36 -y +4
n = 9y2-37y+40