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anonymous

  • one year ago

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  1. Michele_Laino
    • one year ago
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    we can use this exponential function: \[\Large y = A{e^{Bx}}\] where x is the number of years y is the number of snails A, B are two real constants e= 2.71828... is the number of Neperus

  2. Michele_Laino
    • one year ago
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    I have chosen that function, since it is usually used in Physics, nevertheless I think that also your function works well: \[\Large y = a \cdot {b^x}\]

  3. Michele_Laino
    • one year ago
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    where x is the number of years of experimental observation

  4. anonymous
    • one year ago
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    15 years.

  5. Michele_Laino
    • one year ago
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    we can say this: x is such that: \[\Large 0 \leqslant x \leqslant 15\]

  6. Michele_Laino
    • one year ago
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    we need of some other data, for example the number of snails at year x=0

  7. Michele_Laino
    • one year ago
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    I think that we need for realistic data, since we have to model an experiment

  8. Michele_Laino
    • one year ago
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    otherwise, if we have no realistic data, then we can express our answers in terms of the constants a, and b

  9. Michele_Laino
    • one year ago
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    for example the rate r of growth at a certain year x, depends on x itself: \[\Large r = \frac{{f\left( {x + 1} \right) - f\left( x \right)}}{{\left( {x + 1} \right) - x}} = \frac{{a{b^{x + 1}} - a{b^x}}}{1} = a{b^x}\left( {b - 1} \right)\]

  10. Michele_Laino
    • one year ago
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    why is a=10, and b=1.5?

  11. Michele_Laino
    • one year ago
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    furthermore, we have this: \[\Large f\left( {15} \right) = a \cdot {b^{15}}\] is the number of snails after 15 years

  12. Michele_Laino
    • one year ago
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    If those data are typical data of an experiment like yours, then you can use them

  13. Michele_Laino
    • one year ago
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    otherwise we can say this: the function which model the problem is: \[\Large y = a \cdot {b^x}\] where a is the population at x=0 and b is therate of growth

  14. Michele_Laino
    • one year ago
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    models*

  15. Michele_Laino
    • one year ago
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    I don't think so, since we are trying to model an experimental observation, so only realistic data are allowed

  16. Michele_Laino
    • one year ago
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    please, refer to another similar experiment

  17. Michele_Laino
    • one year ago
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    we know that: \[\Large 0 \leqslant x \leqslant 15\] nevertheless the constants a, and b can not be arbitrary

  18. Michele_Laino
    • one year ago
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    ok!

  19. Michele_Laino
    • one year ago
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    please wait, I try to search using google

  20. Michele_Laino
    • one year ago
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    I'm sorry, I have found very difficult articles

  21. Michele_Laino
    • one year ago
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    I continue to search

  22. Michele_Laino
    • one year ago
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    here is an useful article: https://www.illustrativemathematics.org/content-standards/tasks/638

  23. Michele_Laino
    • one year ago
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    @jasmine_15

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