If I know k for a first order equation how can I find the point in time where a given percentage of product has been used up. I only know k and not beginning or ending concentrations.

I don't know what you mean. Is a first order equation a linear equation? And is k a fraction between 0 and 1?

 

Edit: Whoops, I realize why I have no idea what you're talking about. I thought this was math, but you're talking about chemistry.

Well,

 

Because you are using time to determine concentration, then you will have to use the integrated rate law. For a first order reaction, the formula is as follows:

 

ln[A] = -kt + ln[A]0

 

I'd say consider using the formula in terms of percenage. Lets assume the initial molarity is 1M. Graph the equation in terms of [A]. In that case:

 

[A] = e^(-kt) x [A]0 (That is e to the power of negative k times t all multiplied by the initial concentration of one molar.) of course substitute X for t in the equation when graphing. Next find the point in time which you want.. then setup a ratio and find out the percentage left using regular math...

 

hope this helps !