Ok so you weren't given any info about k, but just the half-life. So you used the half-life equation to find k. Very good.
Hint: Now that we have k, is there any equation for a first order reaction that relates concentration of reactant to time and/or k?
Another hint: Pretend the initial concentration of the carcinogen is 100. What then is the concentration of the carcinogen going to be when 99.9% has decomposed (ie reacted)?