How long will it take for an investment that is earning 12.0% interest (compounded continuously) to double in value?

(pt = p0ert)

If you are looking for the time it takes to double your investment but you don't have the amount you are initially investing, you just make up your own numbers.  Seriously. You know the formula so let's use 1000 as the initial investment, and after it doubles it becomes 2000.  So the formula would look like this: 2000=1000*e^(.12)(t). Now the only unknown you have is the t. Start by dividing the 2000 by the 1000 to get a 2 on the right side of the equation:
2=e^.12t.  Now take the natural log of both sides to get: ln2 = ln(e)^.12t. Of course you know that taking a natural log of "e" cancels itself out, leaving
ln2 = .12t.  Now just simply divide the ln2 by .12 to get 5.78 = t (in years)