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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.

Respuesta :

we are given

number of branches is

[tex]B=y-3[/tex]

number of leaves on each branch

[tex]n=2B^2-B[/tex]

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

so, we can plug values

we get

[tex]f(y)=B*n[/tex]

now, we can plug values

[tex]f(y)=(y-3)*(2(y-3)^2-(y-3))[/tex]

now, we can simplify it

[tex]f(y)=2y^3-19y^2+60y-63[/tex]............Answer

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