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Question 185

A scientist is modeling the depletion of a reactant in a chemical solution. The concentration C(t)C(t)C(t) over time ttt is known to be a convex (concave up) function for all t>0t > 0t>0. Identify which of the following qualitative descriptions of the concentration-time graph correctly represents C(t)C(t)C(t).

Graph A: The concentration decreases over time, but the rate of decrease slows down, meaning the gradient C′(t)C'(t)C′(t) is strictly increasing towards zero.

Graph B: The concentration increases over time, but each subsequent increase is smaller than the last, meaning the gradient C′(t)C'(t)C′(t) is strictly decreasing.

Graph C: The concentration increases and then decreases, reaching a clear peak at a local maximum.

Graph D: The concentration decreases over time, and the rate of decrease accelerates, meaning the gradient C′(t)C'(t)C′(t) becomes more negative as ttt increases.

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