\(\mathrm{m(t) = -0.0274(t/7)^2 + 7.3873(t/7) + 75.032}\)The function m gives the predicted body mass \(\mathrm{m(t)}\), in kilograms (kg), of a...

1. TRANSLATE the mathematical statement

• Given: "m(330) is approximately equal to 362"
• This means: \(\mathrm{m(330) = 362}\)
• What this tells us:
  • 330 is the input value (what goes into the function)
  • 362 is the output value (what comes out of the function)

2. INFER what the input and output represent

• From the function definition:
  • \(\mathrm{m(t)}\) = predicted body mass in kilograms
  • \(\mathrm{t}\) = days after the animal was born
• Therefore:
  • Input 330 = 330 days after birth
  • Output 362 = 362 kg of predicted body mass

3. TRANSLATE back to English

• Put it together: "The predicted body mass of the animal was approximately 362 kg 330 days after it was born"
• This matches choice B exactly

Answer: B

Why Students Usually Falter on This Problem

Most Common Error Path:

Poor TRANSLATE reasoning: Students mix up which number represents the input versus the output in function notation. They might think that since 330 appears first in \(\mathrm{m(330) = 362}\), it should also come first when describing the mass, leading them to say "330 kg" instead of recognizing that 330 is the time input.

This may lead them to select Choice A (330 kg at 362 days).

Second Most Common Error:

Weak INFER skill: Students see the \(\mathrm{(t/7)}\) terms in the function and mistakenly think they need to convert 330 to weeks by dividing by 7, not realizing that t is already defined as days and the function handles any necessary conversions internally.

This may lead them to select Choice C (362 kg at 330/7 days).

The Bottom Line:

Function interpretation problems require careful attention to what goes in (input) versus what comes out (output), combined with understanding the real-world meaning of each variable. The mathematical notation tells you the relationship, but you must translate it correctly to English.