Question

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Answer 1

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

Answer 2

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

Answer 3

where x is the number of years of experimental observation

Answer 4

15 years.

Answer 5

we can say this:
x is such that:
\[\Large 0 \leqslant x \leqslant 15\]

Answer 6

we need of some other data, for example the number of snails at year x=0

Answer 7

I think that we need for realistic data, since we have to model an experiment

Answer 8

otherwise, if we have no realistic data, then we can express our answers in terms of the constants a, and b

Answer 9

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

Answer 10

why is a=10, and b=1.5?

Answer 11

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

Answer 12

If those data are typical data of an experiment like yours, then you can use them

Answer 13

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

Answer 14

models*

Answer 15

I don't think so, since we are trying to model an experimental observation, so only realistic data are allowed

Answer 16

please, refer to another similar experiment

Answer 17

we know that:
\[\Large 0 \leqslant x \leqslant 15\]
nevertheless the constants a, and b can not be arbitrary

Answer 18

ok!

Answer 19

please wait, I try to search using google

Answer 20

I'm sorry, I have found very difficult articles

Answer 21

I continue to search

Answer 22

here is an useful article:
https://www.illustrativemathematics.org/content-standards/tasks/638

Answer 23

@jasmine_15