Question

the amount of money in an account with continuously compounded interest. calculated to the nearest tenth of a year how long it takes for an amount of money to double if interest is compounded continuously at 5.2%

Answer 1

You will need this formula:
Years = ln (Total / Principal) / rate
(where "ln" means natural logarithm)
and we'll use $100 and $200 for beginning and ending amount
Years = ln (200 / 100) / rate
Years = 0.69314718056 / .052
Years = 13.3297534723
Rounding to the nearest tenth of a year:
Years = 13.3

Source:
http://www.1728.org/rate2.htm