An accountant is modeling the annual tax expenditures, EEE, in thousands of dollars ttt years after January 1^{\text{st}}1 st 1, start superscript, start text, s, t, end text, end superscript, 200020002000 for a small business using two different models. Both of the accountant's models have tax expenditures of \$5{,}000$5,000dollar sign, 5, comma, 000 on January 1^{\text{st}}1 st 1, start superscript, start text, s, t, end text, end superscript, 200020002000. Model 111 has tax expenditures which increase by \$4{,}000$4,000dollar sign, 4, comma, 000 each year. Model 222 has tax expenditures which increase by a factor of aaa every 555 years. If the models have the same value on January 1^{\text{st}}1 st 1, start superscript, start text, s, t, end text, end superscript, 201020102010, what is the value of aaa