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 AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
