In a bacteria growing experiment, a biologists observes that the number of bacteria in a certain culture triples every 2 hours. After 8 hours, it is estimated that there are 2 million bacteria in the culture. What was the original population of the bacteria?

The answer is  approximately 24,691 bacteria

Explanation:

We were told that after 8 hours the bacterial population was 2 million.

∴ 8 hours ⇒ 2,000,000

We were also told that the population triples after every 2 hours. Which means that the original amount is multiplied by 3 after every 2 hours. Example if the population was 1000 at 1 pm, at 3 pm, the population will be 1000×3 = 3000.

So next, let us find how many two hours are there in 8 hours:

8 = 2+2+2+2

hence there are 4 two hours in 8, so we can conclude that after 8 hours, the population has tripled 4 times. which are at 2 hours, 4 hours, 6 hours and 8 hours. So working backwards from 8 hours, we have;

2,000,000 (after 8 hours)

2,000,000 ÷ 3 = 666,666.67 (after 6 hours)

666,666.67 ÷ 3 = 222,222.22 (after 4 hours)

222,222.22 ÷ 3 = 74,074.07 (at 2 hours)

74,074.07 ÷ 3 = 24,691.35

hence the original population at 0 hours = 24, 691 bacteria

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