The function \(\mathrm{P(t) = 1200(0.5)^t}\) gives the population of bacteria, in thousands, in a petri dish after t hours. Which...
GMAT Advanced Math : (Adv_Math) Questions
The function \(\mathrm{P(t) = 1200(0.5)^t}\) gives the population of bacteria, in thousands, in a petri dish after t hours. Which of the following is the best interpretation of \(\mathrm{P(3) = 150}\)?
1. TRANSLATE the function information
- Given: \(\mathrm{P(t) = 1200(0.5)^t}\) represents bacteria population in thousands after t hours
- Given: \(\mathrm{P(3) = 150}\) (we need to interpret this statement)
- What this tells us: We're looking for the meaning when \(\mathrm{t = 3}\) and \(\mathrm{P = 150}\)
2. INFER what P(3) represents
- \(\mathrm{P(3)}\) means we substitute \(\mathrm{t = 3}\) into the function
- This gives us the population after 3 hours have passed
- The result 150 represents the population value at that time
3. TRANSLATE the result back to context
- Since \(\mathrm{P(t)}\) measures population in thousands
- \(\mathrm{P(3) = 150}\) means: after 3 hours, population = 150 thousand bacteria
- The units are crucial - it's 150 thousand, not just 150 individual bacteria
Answer: A
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students misread or ignore the units specified in the problem setup.
The problem clearly states that \(\mathrm{P(t)}\) gives population "in thousands," but students focus only on the number 150 without considering units. They might think 150 means 150 individual bacteria rather than 150 thousand bacteria, leading them to select Choice D (150 bacteria, not thousands).
Second Most Common Error:
Poor INFER reasoning about function notation: Students confuse input and output values in function interpretation.
Some students mix up which number represents time and which represents population. They might interpret \(\mathrm{P(3) = 150}\) as "after 150 hours, there are 3 thousand bacteria" instead of recognizing that 3 is the input (time) and 150 is the output (population). This leads them to select Choice C.
The Bottom Line:
This problem tests whether students can correctly interpret function values in real-world contexts while maintaining attention to units. Success requires careful translation between mathematical notation and contextual meaning.