Moderate -0.3 This is a straightforward differentiation of an exponential function requiring knowledge that d/dx(a^x) = a^x ln(a), followed by direct substitution. While it requires careful algebraic manipulation to express the answer in the required form ln(a), it's a standard C4 technique with no conceptual challenges or multi-step problem-solving.
2. The current, \(I\) amps, in an electric circuit at time \(t\) seconds is given by
$$I = 16 - 16 ( 0.5 ) ^ { t } , \quad t \geqslant 0$$
Use differentiation to find the value of \(\frac { \mathrm { d } I } { \mathrm {~d} t }\) when \(t = 3\).
Give your answer in the form \(\ln a\), where \(a\) is a constant.
2. The current, $I$ amps, in an electric circuit at time $t$ seconds is given by
$$I = 16 - 16 ( 0.5 ) ^ { t } , \quad t \geqslant 0$$
Use differentiation to find the value of $\frac { \mathrm { d } I } { \mathrm {~d} t }$ when $t = 3$.\\
Give your answer in the form $\ln a$, where $a$ is a constant.\\
\hfill \mbox{\textit{Edexcel C4 2011 Q2 [5]}}