2 year(s) ago, Fatima invested 5,810 dollars. In 1 year(s) from today, she expects to have 8,570 dollars. If Fatima expects to earn the same annual return after 1 year from today as the annual rate implied from the past and expected values given in the problem, then in how many years from today does she expect to have exactly 11,640 dollars? Round your answer to 2 decimal places (for example, 2.89, 14.70, or 6.00).
Please include the math in your answer.