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Mathematics 17 Online
OpenStudy (howard-wolowitz):

Can someone help me here: I'll medal and Thanks!

OpenStudy (howard-wolowitz):

1. A 2. C. 3. B 4. not sure

OpenStudy (howard-wolowitz):

@Michele_Laino

OpenStudy (michele_laino):

I think that we have an exponential growth

OpenStudy (howard-wolowitz):

well excuse me, but i didnt realize they werent the same thing :(

OpenStudy (michele_laino):

I didn't see your data until now, sorry. At first sight I think that we have an exponential growth which can be modeled with the function below: \[\huge y = A \cdot {B^x}\] here we have to check the linear correlation between the subsequent variables: \(\log_{10} y\) and \(x\). If we take the \(logarithm\) of both sides, we can write this: \[\huge {\log _{10}}y = {\log _{10}}A + \left( {{{\log }_{10}}B} \right)x\] which is a linear relation between \( \log_{10}y\) and \(x\)

OpenStudy (michele_laino):

of course, here \(y\) is the number of fish, and \(x\) is the number of months

OpenStudy (michele_laino):

please in order to check my conjecture, try to draw the scatter plot using the data you provided

OpenStudy (howard-wolowitz):

but you wouldn't need to would you, it on the chart provided

OpenStudy (howard-wolowitz):

it shows larger amounts that are being various

OpenStudy (michele_laino):

ok! Then we can continue under the hypothesis of an exponential growth, so we have to compute, using an analytical linear fit, both constants \(\log_{10} A\) and \(\log_{10} B\), and then the values \(A\) and \(B\)

OpenStudy (howard-wolowitz):

maybe my deciamls are off

OpenStudy (michele_laino):

why 2. D ?

OpenStudy (howard-wolowitz):

my decimal was off never mind

OpenStudy (michele_laino):

sincerely I was expecting for a number greater than \(4,738\) as option

OpenStudy (michele_laino):

please try to apply the formulas for linear fit to my model above and then compute the two constants \(A\) and \(B\), after that, you are able to compute the number of fishes at fifth month, by direct substitution

OpenStudy (howard-wolowitz):

ok so would it be 3, and does it have to be rounded

OpenStudy (howard-wolowitz):

its not 4.5

OpenStudy (michele_laino):

why is it 3 ?

OpenStudy (michele_laino):

what is your reasoning, please?

OpenStudy (howard-wolowitz):

i looked at goolge and it seemed it was correct

OpenStudy (michele_laino):

what is the link?

OpenStudy (michele_laino):

I meant the web-link you looked

OpenStudy (michele_laino):

there is not explanation there!

OpenStudy (howard-wolowitz):

hm i see

OpenStudy (michele_laino):

Please, I solve your question using my reasoning and I will explain my solution tomorrow, since it involves a quite long computation

OpenStudy (howard-wolowitz):

hm can we skip it then? how is the next one

OpenStudy (michele_laino):

I don't think that we are able to answer the subsequent questions, if we have not computed both constants \(A,\,B\) above

OpenStudy (howard-wolowitz):

ok

OpenStudy (michele_laino):

ok! :)

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