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.
717 exam-style questions on Edexcel A Level Maths Differentiation, covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change. Each one has a worked solution and a mark scheme showing where the marks go.