**The Doubling Time of Bacterial Culture**

To determine the doubling time of a bacterial culture, we need to calculate the time it takes for the population to double. In this case, the population increased from one thousand to one billion in five hours.

**Step 1: Calculate the Growth Factor**

The growth factor represents the factor by which the population increases over a given period. To calculate the growth factor, we divide the final population by the initial population.

Growth factor = Final population / Initial population

In this case, the initial population is one thousand and the final population is one billion.

Growth factor = 1,000,000,000 / 1,000 = 1,000,000

**Step 2: Calculate the Doubling Time**

The doubling time is the time required for the population to double. It can be determined by dividing the time period by the number of doublings.

Doubling time = Time period / Number of doublings

In this case, the time period is five hours and the number of doublings can be calculated using the growth factor.

Number of doublings = log base 2 (Growth factor)

Using the logarithmic function, we can find the number of doublings:

Number of doublings ≈ log base 2 (1,000,000) ≈ 19.93

Since we cannot have a fraction of a doubling, we round the number of doublings to the nearest whole number, which is 20.

Doubling time = 5 hours / 20 doublings

**Step 3: Convert Hours to Minutes**

To convert the doubling time from hours to minutes, we multiply the doubling time by 60.

Doubling time (minutes) = Doubling time (hours) * 60

Doubling time (minutes) ≈ 5 hours * 60 = 300 minutes

Therefore, the doubling time of the bacterial culture is approximately 300 minutes.