GRE General TestQuantitative ReasoningMedium
A scientist is observing bacterial growth. The number of bacteria in a petri dish doubles every 30 minutes. If there are initially 500 bacteria, how many bacteria will there be after 3 hours?
- A32,000
- B8,000
- C16,000
- D4,000
Show answer & explanationAnswer & explanation
Correct answer: A. 32,000
The bacteria double every 30 minutes. 3 hours = 3 * 60 = 180 minutes. Number of doubling periods = 180 / 30 = 6. Initial bacteria = 500. After 6 doublings: 500 * 2^6 = 500 * 64 = 32,000.
Why the other options are wrong
- B. This is 500 * 2^4, which is incorrect (4 doublings).
- C. This is 500 * 2^5, which is incorrect (5 doublings).
- D. This is 500 * 2^3, which is incorrect (3 doublings).
Exponential Growth
Exponential growth occurs when a quantity increases at a rate proportional to its current value, often characterized by doubling periods.
- Formula: N(t) = N0 * b^(t/T), where N0 is initial amount, b is growth factor, t is total time, T is doubling/halving period.
- For doubling, the base 'b' is 2.
- Common in population growth, compound interest, and radioactive decay (halving).
Memory trick: Growth is like a chain reaction: each step multiplies the last.