Differential equation — Range analysis

Question

Given on , determine the range.

This practice question was inspired by Question 14(a) in the 2024 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: separate or integrate the differential equation, include the constant, then use the initial condition.As , ; as , ; strictly increasing.
State the final answer clearly in the form the question requested.Answer: range .

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

Verification: Horizontal asymptote from above.

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