Precalculus level question. Find the average number of leaves of a tree as a function of height.?

Question

A tree of height y meters has, on average, B branches, where B = y - 5. Each branch has, on average, n leaves where n = 2B2 - B. Find the average number of leaves of a tree as a function of height.

Average number of leaves of a tree =

Answer 1

n = 2B² – B

= B(2B – 1)

= (y – 5)[2(y – 5) – 1]

= (y – 5)(2y – 11)

= 2y² – 11y + 55

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