Question

A bacterial culture is growing exponentially. At 7:00 AM, the number of cells was estimated to be 5.5 X 104 cells. At 11:00 AM, the number of cells increased to 8.7 X 107 cells. What is the generation time in minutes of the bacteria? Please assume we are in the log phase of growth for this bacterial population. Please show your work.

Answer 1

To find the generation time, we need to use the formula:

N = N0 x 2^(t/g)

where:
N0 = initial number of cells
N = final number of cells
t = time elapsed
g = generation time

We can use the information given to solve for g.

At 7:00 AM, N0 = 5.5 x 10^4 cells
At 11:00 AM, N = 8.7 x 10^7 cells
The time elapsed is 4 hours, or 240 minutes.

Substituting these values into the formula, we get:

8.7 x 10^7 = 5.5 x 10^4 x 2^(240/g)

Dividing both sides by 5.5 x 10^4, we get:

1582.7 = 2^(240/g)

Taking the logarithm of both sides (base 2), we get:

log2(1582.7) = 240/g

Solving for g, we get:

g = 240 / log2(1582.7)

Using a calculator, we find that g is approximately 29.3 minutes. Therefore, the generation time of the bacteria is approximately 29.3 minutes.