A tree of height y meters has approximately B branches, where B = y − 4. Each branch has approximately n leaves where n = 4B^2 − B. Find the approximate number of leaves of a tree as a function of height.

Approximate number of leaves of a tree =

I got 4y^2-33y+68, but I'm not sure if thats the final answer..

Question

A tree of height y meters has approximately B branches, where B = y − 4. Each branch has approximately n leaves where n = 4B^2 − B. Find the approximate number of leaves of a tree as a function of height.

Approximate number of leaves of a tree =

I got 4y^2-33y+68, but I'm not sure if thats the final answer..

anonymous · Answer

Plug the value of B in the expression for n, this'll give you the leaves on one branch.$$n=4\times(y-4)^2-(y-4)$$There are a total of B branches so the total number of leaves are B*n. Again plug in the value of B (in terms of y)$$Total.Leaves=(y-4)\times(4\times(y-4)^2-(y-4))$$Now simplify and you'd have the final answer.

anonymous · Answer

What you have is the total number of leaves on 1 branch; to get the total leaves on the tree, multiply it by the number of branches .

anonymous · Answer

I don't get it. I got 4y^2-33y+68

anonymous · Answer

yes, that is from plugging in the value of B in the expression for n. " __Each__ branch has approximately n leaves where n = 4B^2 − B." You plugged in B = y-4 here to get that. Notice the EACH in the problem statement. 
this is the number of leaves on 1 branch and there are B branches, so total leaves on the entire tree are: (Your expression) * (number of branches)

anonymous · Answer

so its 4y^3-49y^2+200y-272

anonymous · Answer

absolutely correct