Exponential growth and decay (bacteria world problem)

a colony of bacteria obeys the function N(t)=N(0)*e^0.2310(t)

where N(0) is the initial size of the population and (t) is time in hours. How long will it take for the colony to double in size?

I'm studying for my math final and I would really appreciate the help and a thorough explanation of how to solve this! thanks!

dN/dt = kN

dN/N = kdt

ʃdN/N (from N to 2N) = kʃdt (from 0 to t)

ln (N) from N to 2N = kt

2.303 log 2 = 0.2310 t

t = 3 hours.