f=ir^t, f=final amount, i=initial amount, r=common ration or "rate", t=times common ration is applied or "time", in this case:
1200=1000r^2 divide both sides by 1000
1.2=r^2 take the square root of both sides
1.2^(1/2)=r so the equation is:
f=1000(1.2)^(t/2), so in 13 hours
f=1000(1.2)^(13/2)
f=1000(1.2)^(6.5)
f≈3271 bacteria (to the nearest whole number)