6. Staphylococcus bacteria has a
doubling time, d ,of 18 minutes.
Calculate how long, t, it will take for
the population to increase, from an
initial population of 400 organisms, to
6400 organisms.
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Since 6400 is 16 * 400, the population has doubled 4 times.
So, it will take 4*18 minutes.
To calculate the time it takes for the population to increase from 400 to 6400 organisms, we need to determine the number of doubling intervals it takes to reach the desired population.
First, let's calculate the doubling time in terms of doubling intervals. The doubling time (d) is given as 18 minutes. Therefore, in 18 minutes, the population will double.
Next, we need to determine the number of doubling intervals required to increase the initial population of 400 to 6400 organisms. We can do this by dividing the final population by the initial population:
Doubling Intervals = log(final population / initial population) / log(2)
Doubling Intervals = log(6400 / 400) / log(2) = log(16) / log(2) = 4 / 0.3010
Doubling Intervals ≈ 13.29
Since we can't have partial doubling intervals, we will round this value up to the nearest whole number. Therefore, it would take 14 doubling intervals to reach 6400 organisms starting from 400 organisms.
Now, we can calculate the total time it takes for the population to increase by multiplying the number of doubling intervals by the doubling time:
Total Time (t) = number of doubling intervals x doubling time
Total Time (t) = 14 x 18 minutes
Total Time (t) ≈ 252 minutes
Therefore, it will take approximately 252 minutes for the population to increase from an initial population of 400 organisms to 6400 organisms.