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