The temperature, θ∘C\theta^\circ\text{C}θ∘C, of a liquid in a cooling tank, ttt minutes after cooling begins, is modeled by the equation
θ=B+150e−kt \theta = B + 150e^{-kt} θ=B+150e−ktwhere BBB and kkk are positive constants. Given that the initial temperature of the liquid is 175∘C175^\circ\text{C}175∘C,
find the value of BBB.
The temperature of the liquid 4 minutes after cooling begins is 67∘C67^\circ\text{C}67∘C.
Show that k=plnqk = p \ln qk=plnq where ppp and qqq are rational numbers to be found.
Hence find
the temperature of the liquid 8 minutes after cooling begins, giving your answer to 3 significant figures,
the rate of decrease of the temperature of the liquid 8 minutes after cooling begins. Give your answer in ∘C min−1^\circ\text{C min}^{-1}∘C min−1 to 3 significant figures.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 311 questions covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
