Digital SATMath: Problem-Solving and Data AnalysisHard
A scientist is tracking the population of a certain bacteria. The population doubles every 4 hours. If the initial population is 500 bacteria, how many bacteria will there be after 20 hours?
- A2,500
- B8,000
- C16,000
- D32,000
Show answer & explanationAnswer & explanation
Correct answer: C. 16,000
The population doubles every 4 hours. Over 20 hours, there will be 20 / 4 = 5 doubling periods. The formula for exponential growth is P(t) = P0 * (growth factor)^(number of periods). Here, P0 = 500, growth factor = 2, and number of periods = 5. So, 500 * 2^5 = 500 * 32 = 16,000.
Why the other options are wrong
- A. This might result from multiplying 500 by 5 (the number of periods) instead of by 2 to the power of 5.
- B. This might result from a calculation error (e.g., 500 * 2^4 = 8000) or miscounting the doubling periods.
- D. This might result from a calculation error (e.g., 500 * 2^6 = 32000) or miscounting the doubling periods.
Exponential Growth (Doubling)
Exponential growth occurs when a quantity increases by a constant factor over equal time intervals, often seen in populations that double or halve.
- Modeled by P(t) = P0 * (growth factor)^(t/T), where T is the doubling period.
- Growth factor for doubling is 2.
- The number of periods is total time divided by the period length.
Memory trick: Initial, then factor to the power of how many times it happens.