How do i fit an equation to a given curve?

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?

[Walter Roberson]

Could you recheck 1) ? It appears to be Nt=rNt with an assignment or comparison between the two sides.

[Kyle]

oops. thank you. its N(t+1)=Nt+rNt

[Kyle]

please help some1!!!

[Walter Roberson]

Nt+rNT -- isn't that the same as (1+r)*N(t) ?

And to check the interpretation of the other part, it is

N(t+1) = N(t)*(1+r*(1-N(t)/k))

right?

[Kyle]

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]

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?

Answer 1

[Walter Roberson]

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.

[Kyle]

sorry. i don't mean to make you spell this out, but i really don't know how to do that. ( how to fit for log(1+r))

[Walter Roberson]

polyfit() with degree 1

[Kyle]

and just plug in n and t too...?

[Walter Roberson]

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.')