GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsHard
A scientist is tracking the population of a certain bacteria culture. Initially, there are 200 bacteria. The population doubles every 3 hours. Which function represents the bacteria population P(t) after t hours?
- AP(t) = 200(2)^(t/3)
- BP(t) = 200(3)^t
- CP(t) = 200(2)^t
- DP(t) = 200 + 2t
Show answer & explanationAnswer & explanation
Correct answer: A. P(t) = 200(2)^(t/3)
This is an exponential growth problem. The initial amount is 200. The growth factor is 2 because it doubles. The doubling period is 3 hours, so the exponent should be t divided by the doubling period (t/3) to reflect how many doubling periods have occurred in t hours. Thus, P(t) = 200(2)^(t/3).
Why the other options are wrong
- B. This implies the population triples every hour, which is incorrect.
- C. This would mean the population doubles every hour, not every 3 hours.
- D. This is a linear growth model, not exponential doubling.
Exponential Growth Function
An exponential growth function models situations where a quantity increases by a fixed percentage or factor over equal time intervals. It's typically represented as y = a(b)^(t/k), where 'a' is the initial value, 'b' is the growth factor, 't' is time, and 'k' is the time period for the growth factor.
- Base 'b' is usually > 1 (e.g., 2 for doubling, 3 for tripling).
- Initial amount 'a' is the y-intercept.
- Exponent (t/k) adjusts for growth occurring over specific intervals (k).
- Used for populations, investments, and compound interest.
Memory trick: Exponential Growth is 'A' times 'B' to the 'T over K'!