A biologist is studying a population of bacteria that triples in size every 3 hours. If the initial population is 200 bacteria, what will be the population after 9 hours?
- A16,200
- B48,600
- C5,400
- D1,800
Show answer & explanationAnswer & explanation
Correct answer: C. 5,400
The population triples every 3 hours. We need to find the population after 9 hours. Number of tripling periods = Total time / Tripling time = 9 hours / 3 hours = 3 periods. Initial population = 200. After 1 period (3 hours): 200 * 3 = 600. After 2 periods (6 hours): 600 * 3 = 1,800. After 3 periods (9 hours): 1,800 * 3 = 5,400. Alternatively, Population = Initial Population * (Tripling Factor)^(Number of Periods) = 200 * 3^3 = 200 * 27 = 5,400.
Why the other options are wrong
- A. Incorrect. This is 200 * 3^4 (after 12 hours), a common error of one extra period.
- B. Incorrect. This is 200 * 3^5 (after 15 hours).
- D. Incorrect. This is the population after 2 tripling periods (6 hours), not 9 hours.
Exponential Growth (Tripling Time)
Exponential growth with a tripling time describes a scenario where a quantity increases by a factor of three over a fixed period. The total growth is calculated by applying the tripling factor for each tripling period that occurs.
- Number of periods = Total Time / Tripling Time.
- Final Amount = Initial Amount * (Tripling Factor)^(Number of Periods).
- The tripling factor is 3.
- This is a form of discrete exponential growth.
Memory trick: Periods count; triples multiply, from start to the sky!