Exponential radioactive decay while original amount increases.

This problem is much trickier than I thought.

I can solve the "easy" half-life problems, such as beginning amount, ending amount and so on. This one's tougher.

Let's suppose you have a substance "X" that has a half life of 30 days. You start out at day zero with 0 grams of "X". For each day, 1 gram of "X" is added to a beaker. (This is a continual process whereby, at the end of each hour, the amount of "X" is increased by 1/24 of a gram, or for each second the amount is increased by 1/86,400 gram. The increases are not done by "chunks".)

Okay so each day, you have an additional gram of "X" and after 5 days (for example) you have 5 grams of "X". But this isn't exactly accurate because some of that 5 grams has already started to decay with a half-life of 30 days.

So, what is the formula for determining how much "X" is present at any particular time?

And since this is my first posting - hello everyone. :)