Practice variation 1 of 3
Differential equation — New ambient and times
Your question
In a room at , coffee is poured at . The temperature (°C) after minutes satisfies .
(i) After 10 minutes the coffee has cooled to . Using separation of variables, solve the differential equation to show that .
(ii) Hence find when the coffee reaches , to the nearest minute.
This practice question was inspired by Question 12(d) in the 2022 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?