OCR MEI C4 — Question 3

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
PaperDownload PDF ↗
TopicFixed Point Iteration
TypeApply iteration to find root (pure fixed point)
DifficultyEasy -1.8 This is a purely mechanical calculation requiring repeated substitution into a given formula with no problem-solving, conceptual understanding, or interpretation needed. Students simply apply the iteration formula three times using a calculator—significantly easier than average A-level questions which typically require some mathematical reasoning or technique selection.
Spec1.09c Simple iterative methods: x_{n+1} = g(x_n), cobweb and staircase diagrams

3 Complete this table to show the next 3 values of the iteration $$x _ { n + 1 } = k x _ { n } \left( 1 - x _ { n } \right)$$ in the case when \(k = 3.2\) and \(x _ { 0 } = 0.5\). Give your answers to calculator accuracy.
\(n\)\(x _ { n }\)
00.5
10.8
20.512
3
4
5

3 Complete this table to show the next 3 values of the iteration

$$x _ { n + 1 } = k x _ { n } \left( 1 - x _ { n } \right)$$

in the case when $k = 3.2$ and $x _ { 0 } = 0.5$. Give your answers to calculator accuracy.

\begin{center}
\begin{tabular}{ | l | l | }
\hline
$n$ & \multicolumn{1}{|c|}{$x _ { n }$} \\
\hline
0 & 0.5 \\
\hline
1 & 0.8 \\
\hline
2 & 0.512 \\
\hline
3 &  \\
\hline
4 &  \\
\hline
5 &  \\
\hline
\end{tabular}
\end{center}

\hfill \mbox{\textit{OCR MEI C4  Q3}}