The count in a bacteria culture was 600 after 10 minutes and 186851 after 30 minutes. Assume the growth can be modelled exponentially by a function of the form $Q(t) = A e^{r t}$, where $t$ is in minutes.

Find the relative growth rate, with at least the first 5 digits after the decimal point entered correctly:
$r=$

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What was the initial size of the culture?

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Find the doubling period (in minutes).

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Find the population after 120 minutes.

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When will the population reach 13000? After minutes.