A bacterial strain is grown in nutrient medium at 37 ˚C under aerobic conditions.The medium is inoculated with 102 cells from a seed culture. If the number ofcells in the culture is 105 after 10 hours of growth, the doubling time of the strain(rounded off to nearest integer) is ____________h
Question
A bacterial strain is grown in nutrient medium at 37 ˚C under aerobic conditions.The medium is inoculated with 102 cells from a seed culture. If the number ofcells in the culture is 105 after 10 hours of growth, the doubling time of the strain(rounded off to nearest integer) is ____________h
Solution
To solve this problem, we need to use the formula for exponential growth, which is N = N0 * 2^(t/g), where:
- N is the final number of cells
- N0 is the initial number of cells
- t is the time of growth
- g is the doubling time
We are given that N = 10^5, N0 = 10^2, and t = 10 hours. We need to solve for g.
First, divide both sides of the equation by N0 to isolate 2^(t/g) on one side:
10^5 / 10^2 = 2^(10/g)
This simplifies to 10^3 = 2^(10/g)
Next, take the logarithm base 2 of both sides to solve for (10/g):
log2(10^3) = 10/g
Rearrange the equation to solve for g:
g = 10 / log2(10^3)
Calculate the value:
g ≈ 10 / 9.97 ≈ 1.003 hours
So, the doubling time of the strain, rounded off to the nearest integer, is approximately 1 hour.
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