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Differentiation

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Question 478

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

Differentiation Questions

  1. A Level
  2. /Maths
  3. /Differentiation

717 exam-style questions on Edexcel A Level Maths Differentiation, 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. Each one has a worked solution and a mark scheme showing where the marks go.

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