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The population of a bacterial culture increases from one thousand to one billion in five hours. The doubling time of the culture (correct to 1 decimal place) is _______ min.
Correct answer is between '14.0,16.0'. Can you explain this answer?
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Explanation:
The formula for calculating the doubling time (td) is given by:
td = ln(2) / r
Where, ln(2) is the natural logarithm of 2 and r is the growth rate.
Step 1: Calculate the growth rate
The growth rate (r) can be calculated using the formula:
r = (ln(Nt) - ln(N0)) / t
Where, Nt is the final population, N0 is the initial population and t is the time taken for the population to grow.
Given, Nt = 1 billion, N0 = 1000 and t = 5 hours
r = (ln(1 billion) - ln(1000)) / 5
r = 29.1 per hour
Step 2: Calculate the doubling time
td = ln(2) / r
td = ln(2) / 29.1
td = 0.0238 hours (convert to minutes)
td = 0.0238 x 60 = 1.43 minutes
Therefore, the doubling time of the bacterial culture is 1.43 minutes. Rounded to one decimal place, the answer is between 14.0 and 16.0 minutes.
The formula for calculating the doubling time (td) is given by:
td = ln(2) / r
Where, ln(2) is the natural logarithm of 2 and r is the growth rate.
Step 1: Calculate the growth rate
The growth rate (r) can be calculated using the formula:
r = (ln(Nt) - ln(N0)) / t
Where, Nt is the final population, N0 is the initial population and t is the time taken for the population to grow.
Given, Nt = 1 billion, N0 = 1000 and t = 5 hours
r = (ln(1 billion) - ln(1000)) / 5
r = 29.1 per hour
Step 2: Calculate the doubling time
td = ln(2) / r
td = ln(2) / 29.1
td = 0.0238 hours (convert to minutes)
td = 0.0238 x 60 = 1.43 minutes
Therefore, the doubling time of the bacterial culture is 1.43 minutes. Rounded to one decimal place, the answer is between 14.0 and 16.0 minutes.
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