GED Mathematical Reasoning TestQuantitative Problem Solving with Rational NumbersHard
A scientist is observing bacterial growth. The number of bacteria doubles every hour. If there are initially 300 bacteria, how many bacteria will there be after 4 hours?
- A4,800
- B1,200
- C9,600
- D2,400
Show answer & explanationAnswer & explanation
Correct answer: A. 4,800
This is exponential growth. Initial bacteria = 300. After 1 hour: 300 * 2 = 600. After 2 hours: 600 * 2 = 1200. After 3 hours: 1200 * 2 = 2400. After 4 hours: 2400 * 2 = 4800. This can also be calculated as 300 * 2^4 = 300 * 16 = 4800.
Why the other options are wrong
- B. This is 300 * 4, which is linear growth, not doubling.
- C. This is 300 * 2^5 (after 5 hours), or a miscalculation.
- D. This is 300 * 2^3 (after 3 hours).
Exponential Growth
Exponential growth occurs when a quantity increases by a constant factor over equal intervals of time. It is characterized by rapid acceleration of growth.
- Formula: Final Amount = Initial Amount × (Growth Factor)^Number of Periods.
- Growth factor for doubling is 2.
- The number of periods is the exponent.
Memory trick: Start small, multiply big, power up fast, like a growth-digit.