Daily Math Puzzle: 2026-08-27
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2026-08-27
In a cutting-edge microbiology lab, scientists are observing a unique self-replicating organism. Its rate of mass increase is directly proportional to its current mass. In an initial experiment, a culture starting with 1 gram of this organism grew to 8 grams in exactly 3 hours. If the scientists started a new experiment with a culture containing 2 grams of the organism, how long would it take for this new culture to grow to a total mass of 16 grams?
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Solution
3 hours — The problem states that the organism's rate of mass increase is directly proportional to its current mass. This is the defining characteristic of exponential growth. A key property of exponential growth is that the time it takes for a quantity to multiply by a certain factor (e.g., double, triple, or increase by 8 times) is constant, regardless of the starting amount.
In the first experiment, the organism grew from 1 gram to 8 grams. This represents an 8-fold increase in mass (8g / 1g = 8). This 8-fold increase took 3 hours.
In the second experiment, the organism starts at 2 grams and needs to grow to 16 grams. This also represents an 8-fold increase in mass (16g / 2g = 8).
Since both experiments require an 8-fold increase in mass, and the growth dynamics are identical (exponential growth), the time taken will be the same.
Therefore, it will take 3 hours for the new culture to grow from 2 grams to 16 grams.
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