anonymous
  • anonymous
.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Michele_Laino
  • 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
Michele_Laino
  • Michele_Laino
I have chosen that function, since it is usually used in Physics, nevertheless I think that also your function works well: \[\Large y = a \cdot {b^x}\]
Michele_Laino
  • Michele_Laino
where x is the number of years of experimental observation

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More answers

anonymous
  • anonymous
15 years.
Michele_Laino
  • Michele_Laino
we can say this: x is such that: \[\Large 0 \leqslant x \leqslant 15\]
Michele_Laino
  • Michele_Laino
we need of some other data, for example the number of snails at year x=0
Michele_Laino
  • Michele_Laino
I think that we need for realistic data, since we have to model an experiment
Michele_Laino
  • Michele_Laino
otherwise, if we have no realistic data, then we can express our answers in terms of the constants a, and b
Michele_Laino
  • Michele_Laino
for example the rate r of growth at a certain year x, depends on x itself: \[\Large r = \frac{{f\left( {x + 1} \right) - f\left( x \right)}}{{\left( {x + 1} \right) - x}} = \frac{{a{b^{x + 1}} - a{b^x}}}{1} = a{b^x}\left( {b - 1} \right)\]
Michele_Laino
  • Michele_Laino
why is a=10, and b=1.5?
Michele_Laino
  • Michele_Laino
furthermore, we have this: \[\Large f\left( {15} \right) = a \cdot {b^{15}}\] is the number of snails after 15 years
Michele_Laino
  • Michele_Laino
If those data are typical data of an experiment like yours, then you can use them
Michele_Laino
  • 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
Michele_Laino
  • Michele_Laino
models*
Michele_Laino
  • Michele_Laino
I don't think so, since we are trying to model an experimental observation, so only realistic data are allowed
Michele_Laino
  • Michele_Laino
please, refer to another similar experiment
Michele_Laino
  • Michele_Laino
we know that: \[\Large 0 \leqslant x \leqslant 15\] nevertheless the constants a, and b can not be arbitrary
Michele_Laino
  • Michele_Laino
ok!
Michele_Laino
  • Michele_Laino
please wait, I try to search using google
Michele_Laino
  • Michele_Laino
I'm sorry, I have found very difficult articles
Michele_Laino
  • Michele_Laino
I continue to search
Michele_Laino
  • Michele_Laino
here is an useful article: https://www.illustrativemathematics.org/content-standards/tasks/638
Michele_Laino
  • Michele_Laino
@jasmine_15

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