Support · Mathematics Extension 1 11–12 – Year 12 · Further applications of calculus
Support Recognise and solve the first order differential equations for exponential growth and decay: dQ/dt = kQ and dQ/dt = k(Q - P)
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Prerequisite dot points
Recognise that the equation dQ/dt = kQ where Q > 0, and its solution Q = Ae^(kt) represent exponential growth when k > 0 and exponential decay when k
Mathematics Advanced 11–12 – Year 12 · Applications of calculus Draft mapping
No checked resources on this prerequisite dot point yet.
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.
Use differentiation to find and interpret the first and second derivatives, dQ/dt and (d²Q)/(dt²), in practical problems where a quantity Q is a function of time t
Mathematics Advanced 11–12 – Year 12 · Applications of calculus Draft mapping
No checked resources on this prerequisite dot point yet.