Question

i know it seems long but it the info being given :S
please help, thanks :)

A branching plant has stems, nodes, leaves and buds.
-there are 7 leaves at each node and at each node, 2 new stems grow. at the end of each final stem, there is a bud

one plant with 3 stages of nodes has 15 stems, 7 nodes, 49 leaves and 8 buds.

one of these plants has 10 stages
work out how many buds and stems it has.

Answer 1

hard to parse the question...

Answer 2

is a node like a knuckle?

Answer 3

I understand it. I had to draw it.

Answer 4

One plant starts with a stem, then has a node. At that node we get two stems going up. If we have one stage of nodes then we end each of those two branches with a bud. giving us one node, 3 stems, 7 leaves and two buds

Answer 5

If we have two stages of nodes, then instead of buds on each stem, we get a node at the end of each stem, and two more branches off each node.
So two stages of nodes is 7 branches, 3 nodes, 4 buds, and 21 leaves.

Answer 6

urm, can you help me work out stage 7 then??
how do i do it???

Answer 7

To figure out how many nodes, we must realize that the nodes keep doubling. 1 stage = 1 node.
2 stages = 1 node + 2 nodes
3 stages = 1 node + 2 nodes + 4 nodes
4 stages = 1 node + 2 nodes + 4 nodes + 8 nodes
et cetera.

Answer 8

isnt there an equation for it or something?

Answer 9

This is like binary numbers, so the formula is 2^n - 1, where n is the number of stages.

Answer 10

Since the branches double one more time than the nodes, the formula for the branches is 2^(n+1) - 1

Answer 11

so its \[2^{11} -1\]
=2047
and which one is this the stem or the buds?

Answer 12

That is the number of branches.

Answer 13

Oh, sorry.
Stems. (I've been calling the stems branches.)

Answer 14

The number of buds is 2^n
In this case 2^10.

Answer 15

so that 1024 for the buds and 2047 for the branches or stems
is that right ?