Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityMedium
A biologist is culturing microorganisms in a petri dish. The initial population is 250 cells. If the population quadruples every 30 minutes, what will the population be after 2 hours?
- A8,000 cells
- B128,000 cells
- C64,000 cells
- D32,000 cells
Show answer & explanationAnswer & explanation
Correct answer: C. 64,000 cells
To solve this, first determine how many 30-minute intervals are in 2 hours. Then, apply the quadrupling factor for each interval to the initial population.
Why the other options are wrong
- A. This would be the population after 1.5 hours (3 intervals).
- B. This would be the population if it quadrupled 5 times, which is incorrect for 2 hours.
- D. This would be the population after 1 hour and 45 minutes (3.5 intervals), or if it doubled each interval.
Exponential Growth
Exponential growth occurs when a quantity increases at a rate proportional to its current value, often characterized by a constant doubling or multiplying period.
- Involves repeated multiplication by a constant factor.
- Can be modeled by N = N₀ * (factor)^(t/T), where N₀ is initial amount, factor is growth factor, t is total time, and T is growth period.
- Leads to very rapid increases over time.
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