C4 January 2011 Q2

2. The current, \(I\) amps, in an electric circuit at time \(t\) seconds is given by \[I = 16 - 16(0.5)^t, \qquad t \geqslant 0\]

Use differentiation to find the value of \(\dfrac{\mathrm{d}I}{\mathrm{d}t}\) when \(t = 3\).

Give your answer in the form \(\ln a\), where \(a\) is a constant. (5)