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 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.
