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

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Homework Help Overview

The discussion revolves around determining an accurate growth rate formula based on a set of X and Y coordinates, specifically in the context of logistic and exponential functions. The original poster expresses confusion regarding the application of these functions to their data, which consists of length and weight measurements with a maximum length constraint.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to identify a suitable growth rate formula, initially suggesting logistic functions but expressing uncertainty about their application. Some participants question the reasoning behind the choice of a logistic model and suggest alternative methods for fitting the data, such as using spreadsheet software for curve fitting. Others propose examining the data graphically to discern the appropriate function type.

Discussion Status

Participants are actively engaging with the original poster's queries, offering suggestions for alternative approaches to data analysis and questioning the assumptions made about the growth model. There is a recognition of the need for further exploration of the data's characteristics, but no consensus has been reached on a specific method or formula.

Contextual Notes

The original poster notes a maximum length constraint for the data, which may influence the choice of growth model. There is also mention of variability in constants when using the calculator's statistical functions, indicating potential challenges in achieving a stable model fit.

the_awesome
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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) = arx. 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 :/
 
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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.
 
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?
 
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.
 
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The stat function on my calculator graphs it for me. It moves like an exponential.
 
the_awesome said:
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