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anonymous
 one year ago
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anonymous
 one year ago
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Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0we 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

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0I have chosen that function, since it is usually used in Physics, nevertheless I think that also your function works well: \[\Large y = a \cdot {b^x}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0where x is the number of years of experimental observation

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0we can say this: x is such that: \[\Large 0 \leqslant x \leqslant 15\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0we need of some other data, for example the number of snails at year x=0

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0I think that we need for realistic data, since we have to model an experiment

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0otherwise, if we have no realistic data, then we can express our answers in terms of the constants a, and b

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0for example the rate r of growth at a certain year x, depends on x itself: \[\Large r = \frac{{f\left( {x + 1} \right)  f\left( x \right)}}{{\left( {x + 1} \right)  x}} = \frac{{a{b^{x + 1}}  a{b^x}}}{1} = a{b^x}\left( {b  1} \right)\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0why is a=10, and b=1.5?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0furthermore, we have this: \[\Large f\left( {15} \right) = a \cdot {b^{15}}\] is the number of snails after 15 years

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0If those data are typical data of an experiment like yours, then you can use them

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0otherwise 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

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0I don't think so, since we are trying to model an experimental observation, so only realistic data are allowed

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0please, refer to another similar experiment

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0we know that: \[\Large 0 \leqslant x \leqslant 15\] nevertheless the constants a, and b can not be arbitrary

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0please wait, I try to search using google

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0I'm sorry, I have found very difficult articles

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0I continue to search

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0here is an useful article: https://www.illustrativemathematics.org/contentstandards/tasks/638
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