How to use curvefitting toolbox to best fit an equation to a curve

I have a set of data points which I must put into different equations to find the value of the unknown coefficients of that particular equation. Is there any particular single way to solve this problem for all the different equations? I tried using the curvefit toolbox, but when I type in the custom equation, the automatic fit is far from perfect. How can I solve the issue?

Some of the equations to which I have to fit the data individualy and find the coefficients of the respective equations are: ;

[Alex Sha]

Adding one more parameter to the fitting function, like y=a*x+b*(1-exp(-c*x))+d, the results will then be much better

Answer 1

[Cris LaPierre]

Your fit equations are constraining the shape of your fit line. If you want a shape that more closely approximates the data, you will need to use a different fit equation.