# Exponential modeling problem

• Mar 30th 2011, 12:53 AM
Bucephalus
Exponential modeling problem
Hi, I"m having trouble working out this problem.
Using data provided, develop a model in the form $\displaystyle y = y_0e^{kt}$ to state the relationship between mass, m, and the length, l, of the fish.

Here is the data:
l 10.1 25.0 32.6 35.4 43.8 45.5 55.7
m 51 236 520 660 1250 1425 2590

I tried doing this with simultaneous equations, using two sets of data points, but that just didn't work. Does anyone know how one would do this?

David.
• Mar 30th 2011, 01:24 AM
CaptainBlack
Quote:

Originally Posted by Bucephalus
Hi, I"m having trouble working out this problem.
Using data provided, develop a model in the form $\displaystyle y = y_0e^{kt}$ to state the relationship between mass, m, and the length, l, of the fish.

Here is the data:
l 10.1 25.0 32.6 35.4 43.8 45.5 55.7
m 51 236 520 660 1250 1425 2590

I tried doing this with simultaneous equations, using two sets of data points, but that just didn't work. Does anyone know how one would do this?

David.

You want a realtionship of the form $\displaystyle m=m_0e^{kl}$. Take logs then you have:

$\displaystyle \log_e(m)=k \times l + \log_e(m_0)$

so now use linear regression using $\displaystyle \log_e(m)$ rather than $\displaystyle$$m$

CB
• Mar 30th 2011, 02:40 AM
Bucephalus
OK I have the linear regression
So I have found that the y intercept of the graph is my $\displaystyle ln(m_0)$ and that the gradient will give me my k.
But I have the y axis as unit increments, 1, 2, 3 and the x axis as 5 unit increments, 5, 10, 15, etc
If I take to vertical lines say from 15 and 20 up to my regression line and then draw across to get their corresponding y-axis values, can I use the gradient formula to get the correct gradient. what I"m asking is the fact that I have used different increments for the y and x axis going to affect me using the gradient formula.

David.
• Mar 30th 2011, 02:45 AM
Bucephalus
Ok, I think that was a silly question. But probably not in the context of using graph paper and working out the gradient graphically, but if I use the gradient forumula I have found that it doesn't matter what the increments are.
thanks.