How to determine rate constant given population growth vs time data?

I have to determine the rate constant of the first order kinetics growth of cancer cells. For a period of 70 seconds, the population growth data has been provided something like this, N = [1 2 3 4.5 7 10 16 29 56 104 and so on..]

The equation is dN/dT = rN

I have plotted the graph in MATLAB which comes out as a sigmoid curve but I have no idea how to calculate the rate constant. Is it as simple as determining the slope for the graph over a region or do I have to use ode45?

I have seen examples where ode45 is used, but in all those examples, both r and N were known and input in the function. How do I go about now?

[David Goodmanson]

Hi Arun,

The equation you show is unrestriced exponential growth (unless r is somehow a function of N) and does not limit out as the sigmoid does. So you will need the correct differential equation to start with.

[Arun]

Hi David, thanks for replying.

I understand your point. The equation should have been different. But, if we do not consider the region of the curve where it flats out, could we possibly determine the rate for a smaller region for eg. from 0 to 20 seconds in the graph?