exponential growth and decay: cuttings of new plants

lori62

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I have read and read the idea of this math and the equations - i am very lost and confused .

here's one of them - A botanist starts with 2 plants. She takes 3 cuttings from each plant to stat new plants. Later she takes 3 cutting from each new plant, and so on.

then a graph -Round of cuttings Number of new plants
0 ?
1 ?
? ?
? ?
? ?
? ?

b) write an equation to model the number of plants, P, in the nth round of cutting

c) How would the graph and equation change in each scenario?explain. the botanist starts with 10 plants. - in each round the botanist takes 2 cuttings from each plant
 
I have read and read the idea of this math and the equations - i am very lost and confused.

here's one of them - A botanist starts with 2 plants. She takes 3 cuttings from each plant to stat new plants. Later she takes 3 cutting from each new plant, and so on.

then a graph -Round of cuttings Number of new plants
0 ?
1 ?
? ?
? ?
? ?
? ?

b) write an equation to model the number of plants, P, in the nth round of cutting

c) How would the graph and equation change in each scenario?explain. the botanist starts with 10 plants. - in each round the botanist takes 2 cuttings from each plant

You put this under "differential equations", but it doesn't belong there, because the variables are discrete. Can you tell us what class you are taking (or where you found this problem, otherwise)? I presume it is not in a differential equations class.

Take it slowly to start with; the first question is meant largely to help you think about what the whole thing means. She starts with 2 plants (after 0 cuttings!). She takes 3 cuttings from each, so how many plants does she have now? 6. But you may find it helpful to initially write what you did to get that, rather than just the number:
Round of cuttingsNumber of new plants
02
12*3 = 6

But to continue, I'd want to add a third column:
Round of cuttingsNumber of new plantsTotal number of plants
022
12*3 = 68
22*8 = 16...

Do a few more rows, and see if you find a pattern; then see if you can explain why that pattern is real, and not just imagined! Once you see what is happening, you can try writing an equation for part (b), and then generalize it for part (c).

By the way, there's a little ambiguity in the problem; at first it seems to say that she cuts only the NEW plants, but later it says EACH PLANT. I've assumed it really means the latter. If I'm wrong, you don't need my third column, and the problem is a little easier. Can you verify the wording? And are there any similar examples that might help us be sure we are interpreting this as intended?
 
I have a suspicion that the student is studying algebra and does not know that differential equations are a branch of calculus. It would be very helpful to be told the name of the course that she is taking and whether she has studied calculus at all. It would also be helpful if we were told what is the name of the chapter that she currently is studying.

I'll also agree that it is not yet clear what the problem is asking. Furthermore, the caption "number of cuttings" is very confusing. On the first iteration, I believe there are six cuttings.
 
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