What is the accurate growth rate formula for a given set of X and Y coordinates?

[the_awesome]

Homework Statement

Hey, been having a lot of hmwk troubles. I haven't really been taught logistic functions or things relating to the matter. I need to figure out an accurate growth rate formula, and to me it seems to be like an exponential.

Note: this is like a table of X and Y coordinates. The maximum the length ( x value) can go to is around 80cm.

Length (cm). 10.1 25 32.6 35.4 43.8 45.5 55.7
Weight (g)... 16 244 542 695 1319 1479 2720

Homework Equations

I'm guessing the logistics equation?
c/ [1 + Ae^-bx]
and
1/[1 + e^-x]

The Attempt at a Solution

I don't really have a clue. I typed it into my calculator, then used the stat function to find a formula for me. It came up with:
5091/[1 + 221.8e^-0.1X

However, I have no idea how the values were calculated. The constant keeps changing, and I've tried using f(x) = ar^x. But that doesn't work either.

Could someone please help me out? Maybe put it into simple terms? All googling about logistics haven't helped me at all :/

 

[badphysicist]

What makes you think that it is a logistics formula? What hints are there? I would suggest that you use something better to fit with than the stat function of your calculator if you don't understand what it is doing and the constant keeps changing. For instance, a spreadsheet program might be good for plotting and curve fitting. It wouldn't help to read up on curve fitting at some point soon. The logistics formula is a bit complicated, so I would try a different function like the last one you gave unless you have a good reason to try something else.

 

[the_awesome]

Its logistic because it has a maximum length. Exponentials continue while logistic ones have maximum, or so i believe?
Is anybody actually willing to help me with this?

 

[Hootenanny]

I echo badphysicist's suggestion of graphing the data. Often, after graphing a set of data it is quite obvious that the form of the graph is close to the characteristic form of a well known set of functions.

In terms of the maximum value, I wouldn't worry about it at this stage. If you're lucky you might find that the maximum value falls out of the function we chose, otherwise we can simply define the function on a restricted domain.

 

[the_awesome]

The stat function on my calculator graphs it for me. It moves like an exponential.

 

[Elucidus]

The stat function on my calculator graphs it for me. It moves like an exponential.

In that case, plot x vs. log y or log x vs. y to see if there is a linear correlation. If so, you can use linear regression to find the line of best fit and "un-log-ing" to get the exponential of best fit.

Just because a maximum value is given does not mean the function is asymptotic to this value (as in the logistic model) but it may just cap out at some point implying a piecewise curve (i.e f is exponential for x <= a and f = 80 for x > a).

--Elucidus