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Differentiation

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Question 169

The mass, MMM kg, of a block of dry ice as it sublimates in a controlled environment ttt hours after the start of an experiment is modelled by the equation

M=12+Pe−kt M = 12 + Pe^{-kt} M=12+Pe−kt

where PPP and kkk are positive constants.

Given that the mass of the block at the start of the experiment was 404040 kg,

a.

find the value of PPP.

[1]
b.

Given also that, exactly 5 hours after the start of the experiment, the mass of the block was 252525 kg,

find the value of kkk to 3 significant figures.

[3]
c.

Using the values for PPP and kkk,

find, according to the model, the rate of change of the mass of the block exactly 8 hours after the experiment started. Give your answer in kg h−1\text{kg}\text{ h}^{-1}kg h−1 to 3 significant figures.

[3]
d.

Explain why, according to the model, the mass of the block cannot fall to 101010 kg.

[1]

Differentiation Questions

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

Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 327 questions covering 12.1 Gradients of Curves, 12.2 Differentiation from first principles, 12.3 Differentiating x^n, 12.4 Differentiating Quadratics, 12.5 Differentiating functions with two or more terms, 12.6 Gradients, Tangents and Normals, 12.7 Increasing and Decreasing Functions, 12.8 Second Order Derivatives, 12.9 Stationary Points, 12.10 Sketching Gradient Functions, and 12.11 Modelling with Differentiation, 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.

Question bank