Question

N a culture of bacteria, a sample is taken at 10:00am and contains 1000 cells per ml. A second sample at 8:00pm has 10,000 cells per ml. What is the generation time ?

Answer 1

Answer:

Solve for n:

logb = logB + nlog2

n = logb - logB

log2

n = logb - logB

.301

n = 3.3 logb/B

G = t/n

Solve for G

G = t

3.3 log b/B

Example: What is the generation time of a bacterial population that increases from 10,000 cells to 10,000,000 cells in four hours of growth?

G = t_____

3.3 log b/B

G = 240 minutes

3.3 log 107/104

G = 240 minutes

3.3 x 3

G = 24 minutes

Answer 2

Given:

The concentration of bacteria at 10:00am (t=0) = Bo = 1000cells/ml

The concentration of bacteria at 8:00pm (t=t) = B = 10000cells/ml

To Find:

The generation time

Solution:

We know that bacterial growth is exponential because each bacteria divides and give rise to one more bacteria which can further divide.

B = Bo X 2ⁿ

Here, n= the number of generations

Substituting the values,

10000 = 1000 X 2ⁿ

Taking log of both sides,

log (10000) = log (1000) + n log 2

or 4 = 3 + n (0.30)

or n = 4-3 / 0.30

= 1/0.30

The generation time = Total time / n

Here total time = 10 hours

So generation time = 10 X 0.30 = 3 hours

Hence, the generation time is 3 hours.