The current, xxx amps, at time ttt seconds after a switch is closed in an electric circuit is modelled by the differential equation
dxdt=k−2x \frac{dx}{dt} = k - 2x dtdx=k−2xwhere kkk is a constant. Initially, there is no current in the circuit.
Solve the differential equation to show that x=k2(1−e−2t)x = \frac{k}{2}(1 - e^{-2t})x=2k(1−e−2t).
In the long term, the current in the circuit approaches 12 amps.
Find the value of kkk.
Find the time, in seconds, for the current to reach 8 amps, giving your answer to 2 significant figures.
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations, 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.
