Microbiology equation problems Please help and show work 1 A

Microbiology equation problems, Please help and show work!

1) A single bacterial cell and its offspring dividing every 15 minutes will reach a population of 1,000,000 cells in how long?

2) If the generation time for E. coli is 20 minutes and you inoculate a flask with 1 cell, how many cells will there be in the flask 24 hours later? Assume no lag period.

Solution

1)Generation time ,G = Time in minutes or hours (t)/ Number of generations (n) /..................Equation (1)

G= 15 minutes , t=?

From equation 1 , we get n= t /G

x= X * 2^{n.............................}.binary fission growth expression equation (2)

where x= number of bacteria at end of time = 1000000

and X=number of bacteria at the beginning of time = 1

From equation 2 , we get n= 3.3 log x/X

substituting the values we get

t/G= 3.3 log (1000000/1)

t/15 = 3.3 *6

t =297 minutes (ans)

2) Generation time(G )= 20 minutes

Initial bacteria (X )= 1

Time (t)= 24 hours = 24*60 minutes

n = t /G

= 24*60 / 20

= 72

Number of generations, n = 3.3 log x/X

72 = 3.3 log x /1

21.8 = log x

x= 10^ 21.8

=6.30* 10²¹ cells ( ans)