.0693
To find this, use the equation A = Pe^rt
This is because it is being compounded continuously rather than a set time.
Use what is given to set up a formula as so:
2000 = 1000e^10r
2000 is put in as it is double of 1000. To solve for r, or the rate, divide both sides by 1000, leaving you with this new equation.
2 = e^10r
In order to get rid of e, you need to do the inverse which is ln or natural log. ln(2 is equal to .693147806
So your new equation can be of variations of that, but I used this one:
.693 = 10r
Now, divide 10 on both sides to get:
r = .0693
Hope this helps!