Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityHard
A scientist is observing the growth of a bacterial colony. The colony initially contains 1,200 bacteria and triples in size every 30 minutes. How many bacteria will be in the colony after 2 hours?
- A10,800
- B291,600
- C32,400
- D97,200
Show answer & explanationAnswer & explanation
Correct answer: D. 97,200
First, determine how many 30-minute intervals are in 2 hours (120 minutes / 30 minutes = 4 intervals). The colony triples in each interval, so the growth factor is 3 raised to the power of the number of intervals (3^4). Initial bacteria × 3^4 = 1,200 × 81 = 97,200.
Why the other options are wrong
- A. This would be the result after 1.5 hours (3 intervals).
- B. This would be the result after 2.5 hours (5 intervals).
- C. This would be the result after 1 hour (2 intervals) if it tripled every 30 minutes, or after 2 hours if it doubled every 30 minutes.
Exponential Growth (Discrete Intervals)
Exponential growth occurs when a quantity increases by a constant factor over equal time intervals. The formula is P(t) = P₀ * (1 + r)ᵗ or P(t) = P₀ * (factor)ᵗ, where 't' is the number of growth intervals.
- P₀ is the initial amount.
- 'factor' is the multiplier for each interval (e.g., 2 for doubling, 3 for tripling).
- 't' must represent the number of growth periods, not necessarily raw time units.
Memory trick: Initial times factor to the power of intervals.