Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityMedium
A biologist is studying a bacterial culture that triples in size every 2 hours. If the culture starts with 500 bacteria, how many bacteria will there be after 6 hours?
- A40,500
- B121,500
- C4,500
- D13,500
Show answer & explanationAnswer & explanation
Correct answer: D. 13,500
The culture triples every 2 hours. In 6 hours, there are 6/2 = 3 tripling periods. So, the initial amount (500) is multiplied by 3 three times: 500 * 3 * 3 * 3 = 500 * 3^3 = 500 * 27 = 13,500.
Why the other options are wrong
- A. This is 500 * 3^4, representing 8 hours of growth.
- B. This is 500 * 3^5, representing 10 hours of growth.
- C. This is 500 * 3^2, representing only 4 hours of growth.
Exponential Growth Rate
Exponential growth occurs when a quantity increases by a constant factor over equal intervals of time. It is often modeled by A = P * r^(t/k).
- P = initial amount
- r = growth factor (e.g., 2 for doubling, 3 for tripling)
- t = total time
- k = time for one growth period
Memory trick: Exponent: Power up, grow fast, like a rocket launching.