The function P gives the estimated number of marine mammals in a certain area, where t is the number of...
GMAT Advanced Math : (Adv_Math) Questions
The function \(\mathrm{P}\) gives the estimated number of marine mammals in a certain area, where \(\mathrm{t}\) is the number of years since a study began. What is the best interpretation of \(\mathrm{P(0) = 1,800}\) in this context?
The estimated number of marine mammals in the area was 102 when the study began.
The estimated number of marine mammals in the area was 1,800 when the study began.
The estimated number of marine mammals in the area increased by 102 each year during the study.
The estimated number of marine mammals in the area increased by 1,800 each year during the study.
1. TRANSLATE the mathematical notation
- Given information:
- \(\mathrm{P(0) = 1,800}\)
- P is a function giving estimated marine mammal population
- t is years since study began
- What this tells us: We need to find what \(\mathrm{P(0) = 1,800}\) means in context
2. INFER what \(\mathrm{t = 0}\) represents
- Since t represents "years since study began"
- \(\mathrm{t = 0}\) means 0 years since study began
- This is exactly when the study began (the starting point)
3. TRANSLATE \(\mathrm{P(0) = 1,800}\) into context
- \(\mathrm{P(0)}\) means the value of function P when \(\mathrm{t = 0}\)
- Since \(\mathrm{t = 0}\) is when the study began
- \(\mathrm{P(0) = 1,800}\) means there were 1,800 marine mammals when the study began
Answer: B. The estimated number of marine mammals in the area was 1,800 when the study began.
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students confuse initial value with rate of change
Students see the number 1,800 and think it represents how much the population changes each year, rather than the starting population. They misinterpret \(\mathrm{P(0)}\) as telling them about the rate of increase instead of the initial count.
This may lead them to select Choice D (1,800 increase per year).
Second Most Common Error:
Poor function notation understanding: Students don't connect \(\mathrm{P(0)}\) to the initial condition
Students may understand that \(\mathrm{t = 0}\) means "when the study began" but fail to recognize that \(\mathrm{P(0)}\) gives the population count at that specific time. They might think \(\mathrm{P(0)}\) represents something else entirely.
This leads to confusion and guessing among the remaining choices.
The Bottom Line:
This problem tests whether students can interpret function notation in context. The key insight is recognizing that \(\mathrm{P(0)}\) gives the "starting value" - the population when \(\mathrm{t = 0}\) (study beginning).
The estimated number of marine mammals in the area was 102 when the study began.
The estimated number of marine mammals in the area was 1,800 when the study began.
The estimated number of marine mammals in the area increased by 102 each year during the study.
The estimated number of marine mammals in the area increased by 1,800 each year during the study.