A student is conducting an experiment in a laboratory to investigate how quickly liquids cool to room temperature - AQA - A-Level Maths Pure - Question 8 - 2019 - Paper 3

Substituting θ = 68 °C and t = 2 into the equation:

68 = 5(4 + λe^{-2k})

This simplifies to:

68 = 20 + 5λe^{-2k}

Thus, rearranging gives:

5λe^{-2k} = 48

From this, we find λe^{-2k} = 9.6.

Next, we also have the initial condition when t = 0:

75 = 5(4 + λe^{0}) => 75 = 5(4 + λ) => 75 = 20 + 5λ => 5λ = 55 => λ = 11.

Now substituting λ back into the previous equation gives:

9.6 = 11e^{-2k} => e^{-2k} = rac{9.6}{11} => e^{-2k} ext{ can be found and then } k ext{ can be determined.}