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)
| Scheme | Marks |
|---|---|
| \(\dfrac{\mathrm{d}I}{\mathrm{d}t} = -16\ln(0.5)0.5^t\) | M1 A1 |
| At \(t = 3\) \(\dfrac{\mathrm{d}I}{\mathrm{d}t} = -16\ln(0.5)0.5^3\) | M1 |
| \(= -2\ln 0.5 = \ln 4\) | M1 A1 |
| (5 marks) |