Support · Mathematics Extension 1 11–12 – Year 12 · Further applications of calculus
Support Describe and examine the graphs of practical situations where the rate of change of a quantity is proportional to the amount Q - P by which the quantity Q exceeds some fixed value P
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Prerequisite dot points
Describe and examine the graphs of practical situations where the rate of change of a quantity is proportional to the quantity
Mathematics Advanced 11–12 – Year 12 · Applications of calculus Draft mapping
No checked resources on this prerequisite dot point yet.
Explain that if the rate of change of a positive quantity Q over time t is proportional to the size of Q, then this may be represented by dQ/dt = kQ where k is the constant of proportionality, and if k > 0 the quantity Q is increasing at a rate proportional to the value of Q at time t, while if k the quantity Q is decreasing at a rate proportional to the value of Q at time t
Mathematics Advanced 11–12 – Year 12 · Applications of calculus Draft mapping
No checked resources on this prerequisite dot point yet.
Use integration to solve practical problems on the rate of change of a quantity Q, where dQ/dt or (d²Q)/(dt²) is given as a function of time t, together with sufficient initial conditions
Mathematics Advanced 11–12 – Year 12 · Applications of calculus Draft mapping
No checked resources on this prerequisite dot point yet.