If you want an investment of $2500 to double, then you want it to get to 2500 x 2 =$5000. From the other information given in the problem, you have A = $5000, P = $2500, and r = 9% = .09. Plug those values into the formula and solve for t:
5000 = 2500 e^(.09t)
Divide by 2500
2 = e^.(09t)
Take the natural logarithm of both sides to get the variable out of the exponent.