Variation 3 · answer guide

Rates of change — Evaluate at a positive time

Question

For , find .

This practice question was inspired by Question 1 in the 2023 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Set up the solution: write the geometric constraint, differentiate every changing quantity with respect to time, then substitute., so .
Match the result to the choices and state the correct option.Therefore option B is correct.

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: Half-life style decay: excess halves each unit of time.

Any mark labels are a TestMum study aid, not an official NESA marking allocation.