GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsMedium
A biologist is studying a bacterial population that doubles every 3 hours. If the initial population is 100 bacteria, what is the population after 12 hours?
- A800 bacteria
- B6400 bacteria
- C3200 bacteria
- D1600 bacteria
Show answer & explanationAnswer & explanation
Correct answer: D. 1600 bacteria
The formula for exponential growth with a doubling period is P(t) = P0 * 2^(t/D), where P0 is the initial population, t is the total time, and D is the doubling period. Here, P0 = 100, t = 12, D = 3. So, P(12) = 100 * 2^(12/3) = 100 * 2^4 = 100 * 16 = 1600.
Why the other options are wrong
- A. This is the population after 9 hours (100 * 2^3).
- B. This is the population after 18 hours (100 * 2^6) or a significant calculation error.
- C. This is the population after 15 hours (100 * 2^5) or a calculation error.
Evaluating Exponential Functions (Doubling)
Calculating the value of an exponential function at a specific point, particularly when dealing with phenomena that double over a fixed period.
- General form: P(t) = P0 * b^(t/D), where b is the growth factor (2 for doubling).
- P0 is the initial amount, t is elapsed time, D is the doubling period.
- The exponent (t/D) represents the number of doubling periods.
Memory trick: Doubling: Start, then multiply by two for each period!