GMAT Focus EditionQuantitative ReasoningMedium
A biologist is tracking the growth of a bacterial colony. The colony doubles in size every 30 minutes. If the colony starts with 100 bacteria, how many bacteria will there be after 2 hours?
- A1600
- B3200
- C800
- D400
Show answer & explanationAnswer & explanation
Correct answer: A. 1600
The colony doubles every 30 minutes. In 2 hours (120 minutes), there are 120/30 = 4 doubling periods. Starting with 100 bacteria, 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
- B. This would be the size after 5 doubling periods (2.5 hours), not 4.
- C. This would be the size after 3 doubling periods (1.5 hours), not 4.
- D. This would be the size after 2 doubling periods (1 hour), not 4.
Exponential Growth (Doubling Time)
Exponential growth with a constant doubling time means a quantity consistently doubles over fixed intervals. The formula is N = N₀ * 2^(t/T), where N₀ is initial quantity, t is total time, and T is doubling time.
- Growth is multiplicative, not additive.
- Doubling periods must be calculated first.
- Can be modeled by N = N₀ * 2^n, where n is the number of doubling periods.
Memory trick: Doubling time means hitting 'times two' over and over.