Answer:
It is going to take around 19 hours and 15 minutes for a single bacteria to grow to fill a thimble with volume 1 cm3.
It will take 57.6 hours to for the volume to fill the entire earth
Step-by-step explanation:
We can say that the volume of the bacteria is a geometric sequence, and each time moment is an arithmetic sequence.
Each geometric sequence has the following format:

In which:
a is the first term
r is the common ratio.
We can find any term of the sequence by the following equation:

Each arithmetic sequence has the following format:

In which:
a is the first term
d is the difference between the terms.
We can find any term of the sequence by the following equation:

How i am going to solve this problem.
We have the sequence that is the volume of the bacteria:
Obs: 



And the following arithmetic sequence that are the time(in hours).




How long will it take for a single bacterium to grow to fill a thimble with volume 1 cm3 ?
I am going to find the value of n for which
, then i find the value at this position in the arithmetic sequence. So




Obs: 


Now, we have to apply these following logarithim proprierties to find the value of n:



log 2 = 0.30
log 3 = 0.48





Lets find
and
in the arithmetic sequence.



It is going to take around 19 hours and 15 minutes for a single bacteria to grow to fill a thimble with volume 1 cm3.
How long will it take for the volume to fill the entire earth 1.08 × 108 km3 ?

So

Lets solve the same way as the first question.





Aside from the proprierties seen in the first exercise, we also have that
log a*b = log a + log b







It will take 57.6 hours to for the volume to fill the entire earth