where is the initial amount of substance and x is the amount of substance left at time t.
What troubles me about this question is that the answer depends on how much of the material was present initially. Let me explain. We wish to find T such that after T days the amount of material is 100 g less than it was, so . Thus:
Which eventually has the solution:
So the time for 100 g to decay depends on . (In fact, if we only have 100 g to start with, then the amount of time is infinite, as you can verify.)