The pressure, PPP kPa, inside a vacuum chamber ttt seconds after a suction pump is activated is modelled by the equation
P=15+Ae−kt P = 15 + Ae^{-kt} P=15+Ae−ktwhere AAA and kkk are positive constants.
Given that the pressure inside the chamber at the instant the pump was activated was 100100100 kPa,
find the value of AAA.
Given also that, exactly 15 seconds after the pump was activated, the pressure was 404040 kPa,
find the value of kkk to 3 significant figures.
Using the values for AAA and kkk,
find, according to the model, the rate of change of the pressure inside the chamber exactly 5 seconds after the pump was activated. Give your answer in kPa s−1\text{kPa}\,\text{s}^{-1}kPas−1 to 3 significant figures.
Explain why, according to the model, the pressure cannot fall to 101010 kPa.
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.
