Answer:
Initial bacterias = 6006000
Altought I believe is safe to assume that the values were 192,000 and 384,000 instead of 192,192,000 and 384,384,000, in that case the initial bacterias is 6000
Step-by-step explanation:
A exponential growth follows this formula:
Bacterias = C*rⁿ
C the initial amount
r the growth rate
n the number of time intervals
Bacterias (55 hours) = 192,192,000
Bacterias (66 hours) = 384,384,000
![Bacterias(55hours)=C*r^{{\frac{55-t}{t}}} \\Bacterias (66hours) = C*r^{\frac{66-t}{t}}}](https://tex.z-dn.net/?f=Bacterias%2855hours%29%3DC%2Ar%5E%7B%7B%5Cfrac%7B55-t%7D%7Bt%7D%7D%7D%20%5C%5CBacterias%20%2866hours%29%20%3D%20C%2Ar%5E%7B%5Cfrac%7B66-t%7D%7Bt%7D%7D%7D)
If you divide both you can get the growth rate:
![\frac{Bacterias (66hours)}{Bacterias(55hours)}=\frac{C*r^{\frac{66-t}{t}}}{C*r^{{\frac{55-t}{t}}}} \\\frac{384,384,000}{192,192,000} =r^{\frac{66-t}{t} -\frac{55-t}{t} } \\2 =r^{\frac{11}{t}}](https://tex.z-dn.net/?f=%5Cfrac%7BBacterias%20%2866hours%29%7D%7BBacterias%2855hours%29%7D%3D%5Cfrac%7BC%2Ar%5E%7B%5Cfrac%7B66-t%7D%7Bt%7D%7D%7D%7BC%2Ar%5E%7B%7B%5Cfrac%7B55-t%7D%7Bt%7D%7D%7D%7D%20%5C%5C%5Cfrac%7B384%2C384%2C000%7D%7B192%2C192%2C000%7D%20%3Dr%5E%7B%5Cfrac%7B66-t%7D%7Bt%7D%20-%5Cfrac%7B55-t%7D%7Bt%7D%20%7D%20%5C%5C2%20%3Dr%5E%7B%5Cfrac%7B11%7D%7Bt%7D%7D)
So with that r = 2 and each time interval correspond to 11 years
Then replacing in one you can get the initial amount of C
![Bacterias (55hours)=C*2^{\frac{55-11}{11} } 192,192,000 = C*32\\C= 6006000](https://tex.z-dn.net/?f=Bacterias%20%2855hours%29%3DC%2A2%5E%7B%5Cfrac%7B55-11%7D%7B11%7D%20%7D%20192%2C192%2C000%20%3D%20C%2A32%5C%5CC%3D%206006000)