GMAT Focus EditionQuantitative ReasoningMedium
A biologist is studying a population of bacteria that triples in size every 4 hours. If the initial population is 100 bacteria, how many bacteria will there be after 12 hours?
- A24,300
- B8,100
- C900
- D2,700
Show answer & explanationAnswer & explanation
Correct answer: D. 2,700
The population triples every 4 hours. In 12 hours, there will be 12 / 4 = 3 tripling periods. So, the initial population of 100 will be multiplied by 3 three times: 100 * 3^3 = 100 * 27 = 2,700 bacteria.
Why the other options are wrong
- A. This is a significantly higher number, likely from an incorrect number of tripling periods or calculation error.
- B. This would be 100 * 3^4 (after 16 hours).
- C. This would be 100 * 3^2 (after 8 hours).
Exponential Growth (Tripling Time)
A phenomenon where a quantity increases by a fixed factor (e.g., triples) over a constant time interval, leading to rapid growth.
- Nt = N0 * (growth factor)^(t/doubling_time)
- For tripling, growth factor is 3.
- The exponent represents the number of tripling periods.
Memory trick: Count the 'tripling' steps, then multiply by the factor each time!