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 AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
