Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityHard
A team of researchers is monitoring the growth of a bacterial colony. The colony initially contains 1,200 bacteria and doubles every 30 minutes. How many bacteria will be in the colony after 2 hours?
- A9,600
- B4,800
- C38,400
- D19,200
Show answer & explanationAnswer & explanation
Correct answer: D. 19,200
Determine the number of doubling periods within 2 hours. Since 2 hours = 120 minutes and it doubles every 30 minutes, there are 120/30 = 4 doubling periods. Then, multiply the initial population by 2 for each doubling period.
Why the other options are wrong
- A. This is after 3 doubling periods (1200 * 2^3 = 9600).
- B. This is after 2 doubling periods (1200 * 2^2 = 4800).
- C. This is after 5 doubling periods (1200 * 2^5 = 38400).
Exponential Doubling
Exponential doubling occurs when a quantity repeatedly multiplies by 2 over fixed intervals. The formula is Initial Quantity * 2^(number of doubling periods).
- The quantity increases very rapidly.
- Number of doubling periods must be calculated first.
- Applies to populations, compound interest, and certain decay processes.
Memory trick: Double, double, toil and trouble, population grows at a bubble.