ACT (Enhanced)MathematicsMedium
A biologist is studying a bacterial population that doubles every 30 minutes. If the initial population is 100 bacteria, which of the following expressions represents the population size after 't' hours?
- A100 * (2t)^2
- B100 * 2^(2t)
- C100 * 2^(t/2)
- D100 * 2^t
Show answer & explanationAnswer & explanation
Correct answer: B. 100 * 2^(2t)
The population doubles every 30 minutes. Since there are 2 periods of 30 minutes in an hour, the exponent needs to reflect this rate. For 't' hours, there are 2t doubling periods.
Why the other options are wrong
- A. This expression uses incorrect order of operations and does not represent exponential growth.
- C. This would be correct if the population doubled every 2 hours, not every 30 minutes.
- D. This would be correct if the population doubled every hour, not every 30 minutes.
Exponential Growth Model
A mathematical model describing growth where the rate of increase is proportional to the current quantity, often represented as P(t) = P0 * b^(t/k).
- P0 is the initial quantity.
- b is the growth factor (e.g., 2 for doubling).
- k is the time it takes for the quantity to grow by factor 'b'.
Memory trick: Grow exponentially, like bacteria in a flask, doubling fast!