Lag phase and exponential growth are different phases, Lag phase is the initial period where cell are been familiarize with growth conditions including medium, next follows exponential phase, in this phase specific growth rate is obtained. Specific growth rates of different strains may compare statistically point by point by nonlinear regression analyses. I have a program to analyse different growth models, if you need any please contact me
you need to measure OD and or growth (plate culture, microscopy or else) and graph a growth curve. Then select the exponential phase and apply the equation given before. If you check the same equation during the growth curve you will find that u change along. We found that depending on salinity and temp from you will get u of 1.1 or 1.3 = a doubling time of 27 to 32 minutes between 3 and 6 hours. After that growth will start slowing down. You can also get growth curves (concentration vs grow) and get umax and KS too.