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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
I have chosen that function, since it is usually used in Physics, nevertheless I think that also your function works well: \[\Large y = a \cdot {b^x}\]
where x is the number of years of experimental observation

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Other answers:

15 years.
we can say this: x is such that: \[\Large 0 \leqslant x \leqslant 15\]
we need of some other data, for example the number of snails at year x=0
I think that we need for realistic data, since we have to model an experiment
otherwise, if we have no realistic data, then we can express our answers in terms of the constants a, and b
for example the rate r of growth at a certain year x, depends on x itself: \[\Large r = \frac{{f\left( {x + 1} \right) - f\left( x \right)}}{{\left( {x + 1} \right) - x}} = \frac{{a{b^{x + 1}} - a{b^x}}}{1} = a{b^x}\left( {b - 1} \right)\]
why is a=10, and b=1.5?
furthermore, we have this: \[\Large f\left( {15} \right) = a \cdot {b^{15}}\] is the number of snails after 15 years
If those data are typical data of an experiment like yours, then you can use them
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
models*
I don't think so, since we are trying to model an experimental observation, so only realistic data are allowed
please, refer to another similar experiment
we know that: \[\Large 0 \leqslant x \leqslant 15\] nevertheless the constants a, and b can not be arbitrary
ok!
please wait, I try to search using google
I'm sorry, I have found very difficult articles
I continue to search
here is an useful article: https://www.illustrativemathematics.org/content-standards/tasks/638

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