## anonymous one year ago .

1. Michele_Laino

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

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

where x is the number of years of experimental observation

4. anonymous

15 years.

5. Michele_Laino

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

6. Michele_Laino

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

7. Michele_Laino

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

8. Michele_Laino

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

9. Michele_Laino

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

why is a=10, and b=1.5?

11. Michele_Laino

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

12. Michele_Laino

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

13. Michele_Laino

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

models*

15. Michele_Laino

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

16. Michele_Laino

please, refer to another similar experiment

17. Michele_Laino

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

18. Michele_Laino

ok!

19. Michele_Laino

please wait, I try to search using google

20. Michele_Laino

I'm sorry, I have found very difficult articles

21. Michele_Laino

I continue to search

22. Michele_Laino

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

23. Michele_Laino

@jasmine_15