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−ktwhere PPP and kkk are positive constants.
Given that the mass of the block at the start of the experiment was 404040 kg,
find the value of PPP.
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.
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.
Explain why, according to the model, the mass of the block cannot fall to 101010 kg.
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.
