How long would it take to earn $7000 on a 3500 dollar investment at rate of 7.8% compounded continuously?

Question

Would it be something like this:
7000=3000*(1+0.078)/? not sure about what to divided by???

Help-I'm really confused!!!!

Answer 1

dx/dt =.078 x
dx/x = .078 dt
ln x = .078 t
x =X e^(.078 t)

7000 = 3500 e^(.078 t)
ln 2 = .078 t
t = .693/.078 = 8.9 years