ATI TEAS (Test of Essential Academic Skills) Version 7MathematicsMedium
A researcher is tracking the growth of bacteria. The population doubles every 30 minutes. If the initial population is 100 bacteria, how many bacteria will there be after 2 hours?
- A3200
- B1600
- C800
- D400
Show answer & explanationAnswer & explanation
Correct answer: B. 1600
2 hours = 120 minutes. Since the population doubles every 30 minutes, there are 120/30 = 4 doubling periods. Initial population = 100. After 1 period: 100 * 2 = 200. After 2 periods: 200 * 2 = 400. After 3 periods: 400 * 2 = 800. After 4 periods: 800 * 2 = 1600. Alternatively, 100 * (2^4) = 100 * 16 = 1600.
Why the other options are wrong
- A. This is after 5 doubling periods (2.5 hours).
- C. This is after 3 doubling periods (1.5 hours).
- D. This is after 2 doubling periods (1 hour).
Exponential Growth (Doubling)
A pattern of growth where a quantity increases by a fixed percentage or factor over a constant time interval.
- Common in biology (bacteria, cell division) and finance (compound interest).
- The growth rate is proportional to the current size.
- Can be modeled by the formula N(t) = N0 * (growth_factor)^(t/doubling_time).
Memory trick: Exponential growth: multiply by the factor, each time period.