Estimation of cell count of E.coli culture
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.