Time Weighted Average numerator expression?

• A. (C1 + T1) + (C2 x T2)
• B. (C1 x T1 x C2 x T2)
• C. (C1 + T1 + C2 + T2)
• D. (C1 x T1) + (C2 x T2) + ...

Answer: (D)

Time weighted average requires weighting each concentration by how long you’re exposed at that level, then combining those contributions. The numerator is the sum of each concentration multiplied by its corresponding time at that concentration. In other words, you take C1 × T1 for the first interval, add C2 × T2 for the second interval, and continue for all segments. This reflects how longer exposure at a given concentration contributes more to the overall average.

For example, 0.5 mg/m3 for 8 hours and 1 mg/m3 for 16 hours gives a numerator of 0.5×8 + 1×16 = 4 + 16 = 20 mg·h/m3. The denominator would be the total time (24 h), giving the time-weighted average as 20/24.

Forms that simply add concentrations (or times) or multiply all values together don’t account for the duration of each exposure and therefore aren’t correct for the numerator.