2n/7 is more intuitive because the machines double exactly every 7 days, as opposed to finding some generic real number exponent and scalar multiple when using e as the base. this way you get an exact solution of 3652.5 - 7/ln(2) instead of just getting arbitrary approximations on a calculator. Those arbitrary approximations will still give you 7/ln(2) but exact solutions are nicer and this gets you the exact one quicker.
Also, I get that 3652.5 is the average number of days in 10 years, but Duncan said "how many can you make in 10 years", so personally I would choose the longest version of 10 years possible, which has 3 leap years and 3653 days, which is what I used in my own solution