Since you are not integrating the differential equation, this is a simple nonilinear parameter estimation problem.
Try this:
T = 270:280; % Create ‘T’
dNdT = rand(size(T)); % Create ‘dNdt’
a = 42; % Create ‘a’
deltaE = 3; % Create ‘deltaE’
R = 8.3145;
objfcn = @(b,T) a.*exp(-deltaE./(R*T)) .* (1 - b); % Objective Function
B = fminsearch(@(b) norm(dNdT - objfcn(b,T)), 10); % Estimate Parameter
It might be possible to solve it as a linear problem, however that is not obvious to me just now.
Experiment to get the result you want.
