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.
115 exam-style questions on CCEA A Level Maths 1.6 Differentiation, covering 1.6.1 Differentiation, 1.6.2 Differentiation, 1.6.3 Differentiation, 1.6.4 Differentiation, 1.6.5 Differentiation, 1.6.6 Differentiation, and 1.6.7 Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.