3600 years.
Since 65% of the carbon-14 is remaining, we need to get the logarithm to base 2 of 0.65 to determine how many half lives have expired. So: log(0.65)/log(2) = -0.187086643/0.301029996 = -0.621488377
So we know that 0.621488377 half-lives has gone by to the bone sample. Now we just need to multiply by the half-life of carbon-14 which is 5730 years. So: 0.621488377 * 5730 = 3561.128399 years. Rounding to the nearest 100 years gives us 3600 years.
