40 milliliters of a well-stirred broth is inoculated with 8 mg of bacteria. Init

Question

40 milliliters of a well-stirred broth is inoculated with 8 mg of bacteria. Initially, the inoculated broth is kept at room temperature for 2 hours. At that time a 10 milliliter sample is removed and found to contain 2.9 mg of bacteria. The remaining broth is placed in a refrigerator. It is analyzed 24 hours later and found to contain 10.9 mg of bacteria. Assume the growth is Malthusian at each of the two temperatures (in and out of the refrigerator).

The doubling time of the bacteria at room temperature is------------------------- hours.

The doubling time of the bacteria at the refrigerator temperature is------------------------------ hours.

Explanation / Answer

40 ml of broth was inoculated with 8mg of bacteria.Q1 = (8/40=0.2mg/ml)

10 ml was withdrawn after 2 hours & found to contain 2.9mg of bacteria: Q2 = (0.29 mg/ml)

Therefore, the doubling time at room temperature is:

Td = (t2 - t1) x {log2/[log(Q2/Q1)]}

= 2 x {log2/[log(0.29/0.2]}

=2 x (0.3/0.16) =3.76 hour (Ans)

After 24 hours 30ml contained 10.9 mg bacteria. Q3 = (10.9/30 = 0.36 mg/ml)

Doubling time at the refrigerator temperature:

Td = (t2 - t1) x {log2/[log(Q3/Q2)]}

= (24-2) x {0.3/[log(0.36/0.29) ]}

= 70.28 hour (Ans)

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