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Can I get some help with an estimation of a cell count in a culture of E.coli cells if we assume we begin with $10^6$ cells, that they divide every 30 minutes and they are incubated for 12 hours?

I do not know how to do the calculation with a start number that is not 2, if it was it would just be $2^{24}$. But how is it done when the starting number of cells is $10^6$?

Is it $(10^6)^{24}$?

Thank you!

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You start with $10^6$ cells. After 30 min they double, so there are $2⋅10^6$ cells. After another 30 minutes they double again, so there are $2⋅2⋅10^6$ or $2^2⋅10^6$ cells. After three doubling periods, the number of cells is $2^3⋅10^6$. Doing this, the equation for exponential growth should become evident. All you must do now is determine the number of doubling periods in 12 hours.

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