Support · Mathematics Extension 1 11–12 – Year 12 · Further applications of calculus
Support Use dQ/dt = k(Q - P), Q = P + Ae^(kt) and the graph of Q = P + Ae^(kt) for t ≥ 0, where k > 0 or k and A > 0 or A, to model and solve problems where a limiting value of Q exists, including Newton’s Law of Cooling and ecosystems with a natural carrying capacity, and justify conclusions in the context of the problem
Resources for the prerequisite content of this dot point: earlier-stage (or earlier sub-level) dot points in the same strand that students usually need first. Use these to fill gaps before or alongside the core lesson.
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Prerequisite dot points
Model and solve growth and decay problems in various contexts using dQ/dt = kQ, Q = Ae^(kt) and the graph of Q = Ae^(kt) for t ≥ 0, and justify conclusions in the context of the problem
Mathematics Advanced 11–12 – Year 12 · Applications of calculus Draft mapping
No checked resources on this prerequisite dot point yet.
Graph y = f'(x) and y = f''(x) for a function y = f(x), given only a graph of y = f(x)
Mathematics Advanced 11–12 – Year 12 · Applications of calculus Draft mapping
No checked resources on this prerequisite dot point yet.
Graph the function Q = Ae^(kt), where k > 0 and k and A > 0 and A, with and without graphing applications, and identify any asymptotes
Mathematics Advanced 11–12 – Year 12 · Applications of calculus Draft mapping
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
- Interactive toolEnrichmentGeoGebra ClassicUse it for: Dynamic geometry and graphing for constructions and proofs.