How do i fit an equation to a given curve?

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Kyle
Kyle 2014-2-2
评论： Walter Roberson 2014-2-2
I've been giving the following data.
t=[0:14]';
n=[105 118 139 164 189 214 240 265 290 316 330 348 363 369 373]';
and have been asked to fit the following two equations to this set of data.
1) N(t+1)= Nt=rNt
and
2) N(t+1)=Nt(1+r(1-Nt/k))
any advice on how to go about it. I can use polyfit and polyval to determine a fitted graph. but i have no idea how to relate it to the above equations. is there anyway i can determine an "r" value that will give me the best fitted results?
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Kyle
Kyle 2014-2-2
no its not the same. these are FDE's so the t is supposed to be a subscript. so each n ( in this example) is a population size at each interval of t. did u follow that. sorry its difficult to type it out.
Kyle
Kyle 2014-2-2
ohhh wait.you're just simplifying it, right? and yet your interpretation of the 2nd equation is correct. what are you trying to get at tho?

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Walter Roberson
Walter Roberson 2014-2-2
When
N(t+1) = (1+r)*N(t)
then
N(t) = (1+r)^t * N(0)
Take log...
log(N(t)) = t * log(1+r) + log(N(0))
This puts you in a position to do a linear fit to determine log(1+r), from which you can determine r.
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Walter Roberson
Walter Roberson 2014-2-2
p = polyfit(t, log(n), 1);
r = exp(p(1)) - 1;
N0 = exp(p(2));
plot(t, (1+r).^t * N0, 'b', t, n, 'k.')

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