A particular type of bacteria can under optimal conditions double every 20 minut

Question

A particular type of bacteria can under optimal conditions double every 20 minutes. Imagine that just after a 6 L culture became saturated with bacteria, a researcher poured the saturated culture into an amount of fresh culture that was three times the initial amount of culture (e.g., 5 L original culture is poured into 15 L of fresh culture). How long would it take for this total volume of culture to become saturated again, assuming that optimal conditions prevailed and that no cells died? Enter your answer to the nearest minute.

Explanation / Answer

The culture doubles after 20 minutes

Let the saturated concentration = x / L

So the concentration in 6L = 6x

Now the dilution is upto 18L

Saturated concentration required = x / L

So the concentration in 18L should be 18x

(i) from 6x to 18x the concentration need to be raised

(ii) time required to raise the concentration from 6x to 12x = 20minutes

(iii) the time required to raise the concentration from 12x to 18x = 10minutes

total time required = 20 + 10 = 30 minutes

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