I think you might be looking for something like this. First, here's a plot of your data that you want to fit.
By clicking Analyze>Modeling>Nonlinear, you get the following dialog box.
Click the Model Library button and you'll see a variety of built-in models. You can even add your own custom formulas by editing a dll although I forget which one off the top of my head. There's one titles First Order Decay Kinetics and you can view the formula as well as a graph with sliders as seem below. You can click the 'Make Formula' button on the left graph and a new dialog appears asking you to input the x and y variables. Once that is done the selected decay formula with be shown with your data as well as more sliders for 'What-If' scenarios. These can be used as your initial estimates for theta1 and theta2 which you must provide for a nonlinear fit. Now you have a new column in your JMP data set containing the formula with initial estimates.
Go back to Analyze>Modeling>Nonlinear, fill in the following and click 'OK'. I took the liberty of editing the formula such that there was no theta3 parameter (i.e., assuming it can't go below zero).
You'll get the following. Click 'Go' and you'll see the 'best' fit based on the starting parameters and method of convergence. You can save the prediction formula by accessing the red triangle. Now you have your formula saved in the original table.
Hope this helps.
Dave