Question

A tree of height y meters has, on average, upper b branches, where upper b equals y minus 3. Each branch has, on average, n leaves where n equals 2 upper b superscript 2 baseline minus upper
b. Find the average number of leaves on a tree as a function of height.

Answer 1

we are given

number of branches is

$B=y-3$

number of leaves on each branch

$n=2B^2-B$

the average number of leaves = (number of branches)*(number of leaves on each branch)

so, we can plug values

we get

$f(y)=B*n$

now, we can plug values

$f(y)=(y-3)*(2(y-3)^2-(y-3))$

now, we can simplify it

$f(y)=2y^3-19y^2+60y-63$............Answer