Mycobacterium tuberculosis is pathogenic bacteria that infec

Mycobacterium tuberculosis is pathogenic bacteria that infects lungs and other organs to cause tuberculosis, a common and often deadly disease. M. tuberculosis has an average generation time of 20 hours/generation. Calculate how long it would take to produce 106 M. tuberculosis cells from one lonely original bacteria under these conditions. Show all calculations, always include units, do not round off any numbers during your calculations. Round your answer to provide the answer with a precision of 1 hour. Express your final answer in days and hours; e.g. 4.16 days (no), 100 hrs (no), 4 days and 4 hrs (yes).

Solution

. =Mycobacterium tuberculosis has a generation time of 20 hours, also known as the doubling time.

It can be calculated by the following formula:

N= K*2^(t/d)

Alternatively, it can be calculated by the following formula

Number of generations = log (_{cells at the end of incubation)}- log_{(cells at the beginning of incubation)}

Therefore , (log 1.06*10^8) - (log 1)/ 0.301

= (8.0253-0)/0.301

= 26.662

Here, log of 106 million is 8.0253, and log 1 is 0

26.6621 number of generations will be required to reach 106million cells .

To convert number of generations into time in minutes we use the following formula

60 min * hours / number of generations = generation time

Here, the generation time and number of generations is already known. So to calculate the hours / time required for generation :

Hours= generation time* number of generations

Here, we are not including 60 minute in the calculation as the generation time is already given in hours.

Hours = 20 hr/ generation * 26.6621

= 533.242 hours

To convert into days we divide it with 24

533.242/24

= 22. 22 days

Thus the answer is 22 days and 9 hours (8.72 hours).