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3.6 Differentiation (A-level only)

3.6 Differentiation (A-level only)

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Question 129

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−kt

where BBB and kkk are positive constants. Given that the initial temperature of the liquid is 175∘C175^\circ\text{C}175∘C,

a.

find the value of BBB.

[2]
b.

The temperature of the liquid 4 minutes after cooling begins is 67∘C67^\circ\text{C}67∘C.

Show that k=pln⁡qk = p \ln qk=plnq where ppp and qqq are rational numbers to be found.

[3]
c.

Hence find

the temperature of the liquid 8 minutes after cooling begins, giving your answer to 3 significant figures,

[3]
d.

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.

[3]
Markscheme

3.6 Differentiation (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6 Differentiation (A-level only)

333 exam-style questions on WJEC A Level Maths 3.6 Differentiation (A-level only), covering 3.6.1 Differentiation (A-level only), 3.6.2 Differentiation (A-level only), 3.6.3 Differentiation (A-level only), 3.6.4 Differentiation (A-level only), 3.6.5 Differentiation (A-level only), 3.6.6 Differentiation (A-level only), 3.6.7 Differentiation (A-level only), and 3.6 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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