Question 313164
How long will it take an investment to double if it is invested at a 5% annual interest rate and compounded continuously? 
.
You forgot the "initial principal" in your formula...
.
Continuously compounded interest:
P=(Po)e^rt
Where
P is the amount after time t
Po is the initial investment
r is the rate 
t is the time
.
So, the "trick" is to assign a variable to the intial investment:
Let x=initial investment (Po)
So, when we double it we should have:
2x = final amount (P)
.
Plug in what we know into:
P=(Po)e^rt
2x = xe^(.05t)
Now, we solve for t:
We begin by dividing both sides by x:
2 = e^(.05t)  (notice our variable is gone!)
ln(2) = .05t
ln(2)/.05 = t
13.86 years = t