How do i do exponential growth w/o the rate

Heres the problem: In 2002 participants = 500. In 2012, participants = 3600. Assuming participation grows exponentially, estimate participation in 2015. Round to 4 decimals

3600 = 500e^10k
ln 7.2 = 10k
k = 0.1974
when t = 13
A = 500e^(13*0.1974) = 6,508

You do have the rate. In 10 years it grows by a factor of 3600/500. That tells you the rate.

P/P0 = e^(r*t)
ln(P/P0) = r * t
ln(3600/500) = r * 10