For an $\textit{E.coli}$ culture in the exponential phase of growth, optical density (OD) at $540$ nm is $0.3$ at $2$ hours and $0.6$ at $4$ hours. Assuming that the measured OD is linearly proportional to the number of $\textit{E.coli}$ cells, the growth rate (per hour) for this culture is _________.