Noah borrows $2000$2000dollar sign, 2000 from his father and agrees to repay the loan and any interest determined by his father as soon as he has the money. the relationship between the amount of money, aaa, in dollars that noah owes his father (including interest), and the elapsed time, ttt, in years, is modeled by the following equation. a=2000e^{0.1t}a=2000e 0.1t a, equals, 2000, e, start superscript, 0, point, 1, t, end superscript how long did it take noah to pay off his loan if the amount he paid to his father was equal to $2450$2450dollar sign, 2450? give an exact answer expressed as a natural logarithm.