Question

Consider a tree of heigh y 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. Picture below

Answer 1

Hello,

Height: y
Number of branches: B=y-3
Number of leaves on one branche:n=10B²-B

Number of leaves on the tree:
nb=n*B=(10B²-B)*B=10B^3-B²

=10(y-3)^3-(y-3)²=(y-3)²[10(y-3)-1]=(y-3)²(10y-31)

a) if y=9 then nb=(9-3)²*(10*9-31)=36*59=2124.