1. Exponential modeling problem

Hi, I"m having trouble working out this problem.
Using data provided, develop a model in the form $y = y_0e^{kt}$ 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.

2. Originally Posted by Bucephalus
Hi, I"m having trouble working out this problem.
Using data provided, develop a model in the form $y = y_0e^{kt}$ 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 $m=m_0e^{kl}$. Take logs then you have:

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

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

CB

3. OK I have the linear regression

So I have found that the y intercept of the graph is my $ln(m_0)$ 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.

4. 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.