Practice variation 3 of 3
Differential equation — Alternate equilibrium multiparts
Your question
For :
(i) Explain why a solution with can never reach .
(ii) Describe the long-term behaviour of the solution through .
(iii) Find the population at which the growth rate is largest, using calculus.
This practice question was inspired by Question 13(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.
Before you check
- Have you stated every choice or assumption?
- Can another student follow each line?
- Did you verify the final result independently?