Why would you need to approximate a given function using another (exponential) function, and only then solve for a time?
Use fzero, assuming that you already have a function.
Is it that you only have data points? Then you will need to postulate a model. How can we know if an exponential is right for your problem though? Only you know that. Anyway, if so, then you already know you need to use fit, so wtp? read the help and examples for the curve fitting toolbox.