A culture has 3000 cells at 10:00 and 48 000 cells at 12:00.

For exponential counts, $\ln N = \ln N_0 + rt$: np.polyfit(t, np.log(N), 1) returns the slope $r$ and the intercept $\ln N_0$. Doubling time $= \dfrac{\ln 2}{r}$. curve_fit(model, t, N, p0=guess) returns the parameters after t, in order, that make the sum of squared misses smallest.