A tree of height y meters has approximately B branches, where B = y − 7.
Each branch has approximately n leaves where n = 9(B^(2)) − B. Find the approximate number of leaves of a tree as a function of height.

Question

A tree of height y meters has approximately B branches, where B = y − 7. 
Each branch has approximately n leaves where n = 9(B^(2)) − B. Find the approximate number of leaves of a tree as a function of height.

aravindg · Answer

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anonymous · Answer

Please help?

tkhunny · Answer

We have $n  = 9B^{2} - B$.  This is the number of leaves on each branch.
We have $B = y - 7$.  This is the number of branches on a tree.

Total Leaves, then, should be $n*B = (9B^{2} - B)\cdot (y-7)$

Since we are required to find a function of ONLY the height of the tree, we need to get rid of those Bs.  This can be done by substitution since we know $B = y - 7$

$n*B = (9B^{2} - B)\cdot (y-7) = [9(y-7)^{2} - (y-7)]\cdot (y-7)$

See how that worked?  You have some algebra in your future.

anonymous · Answer

After solving through i got: $$9y ^{3}-187y ^{2}+1337y-3136$$ is this my answer or do i need to solve for a value?