The e. coli bacteria has a volume of 6 µm3 . in optimal conditions, an e. coli bacteria will double about every 30 minutes. under these conditions, how long will it take for a single bacterium 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 ?

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

h= 12 inches

step-by-step explanation: