Given that a tree of height [tex]y[/tex] meters has
approximately [tex]B[/tex] branches, where [tex]B=y-1[/tex]. Each branch has
approximately [tex]n[/tex] leaves where [tex]n=8B^2-B[/tex].
(b) Consider a tree of height [tex]y[/tex] meters. Use the model
above to find an expression for the approximate number of leaves on
the tree. Give your answer in terms of y.
The approximate number of branches on the tree of height [tex]y[/tex] is given by [tex]B=y-1[/tex]
The approximate number of leaves on each branch is
[tex]n=8B^2-B\\ \\=8(y-1)^2-(y-1)\\ \\=8(y^2-2y+1)-y+1\\ \\=8y^2-16y+8-y+1\\ \\=8y^2-17y+9[/tex],
Given that there are [tex]B=y-1[/tex] branches on the three.
Therefore, the approximate number of leaves on the tree is given by
[tex](y-1)(8y^2-17y+9) \\ \\ =8y^3-17y^2+9y-8y^2+17y-9 \\ \\ =8y^3-25y^2+26y-9[/tex]
