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anonymous

  • 5 years ago

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.

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  1. amistre64
    • 5 years ago
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    hard to parse the question...

  2. amistre64
    • 5 years ago
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    is a node like a knuckle?

  3. Stacey
    • 5 years ago
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    I understand it. I had to draw it.

  4. Stacey
    • 5 years ago
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    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

  5. Stacey
    • 5 years ago
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    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.

  6. anonymous
    • 5 years ago
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    urm, can you help me work out stage 7 then?? how do i do it???

  7. Stacey
    • 5 years ago
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    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.

  8. anonymous
    • 5 years ago
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    isnt there an equation for it or something?

  9. Stacey
    • 5 years ago
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    This is like binary numbers, so the formula is 2^n - 1, where n is the number of stages.

  10. Stacey
    • 5 years ago
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    Since the branches double one more time than the nodes, the formula for the branches is 2^(n+1) - 1

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

  12. Stacey
    • 5 years ago
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    That is the number of branches.

  13. Stacey
    • 5 years ago
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    Oh, sorry. Stems. (I've been calling the stems branches.)

  14. Stacey
    • 5 years ago
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    The number of buds is 2^n In this case 2^10.

  15. anonymous
    • 5 years ago
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    so that 1024 for the buds and 2047 for the branches or stems is that right ?

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