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.
