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.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 327 questions covering 12.1 Gradients of Curves, 12.2 Differentiation from first principles, 12.3 Differentiating x^n, 12.4 Differentiating Quadratics, 12.5 Differentiating functions with two or more terms, 12.6 Gradients, Tangents and Normals, 12.7 Increasing and Decreasing Functions, 12.8 Second Order Derivatives, 12.9 Stationary Points, 12.10 Sketching Gradient Functions, and 12.11 Modelling with Differentiation, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
