Moderate -0.3 This is a straightforward application of Euler's method with given starting point, step length, and function. It requires only mechanical iteration (two steps) with no conceptual difficulty beyond knowing the basic formula y_{n+1} = y_n + h·f(x_n). The calculation is routine for FP1 level, though the 6 significant figures requirement demands careful arithmetic.
2 A curve satisfies the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = 2 ^ { x }$$
Starting at the point \(( 1,4 )\) on the curve, use a step-by-step method with a step length of 0.01 to estimate the value of \(y\) at \(x = 1.02\). Give your answer to six significant figures.
2 A curve satisfies the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = 2 ^ { x }$$
Starting at the point $( 1,4 )$ on the curve, use a step-by-step method with a step length of 0.01 to estimate the value of $y$ at $x = 1.02$. Give your answer to six significant figures.
\hfill \mbox{\textit{AQA FP1 2008 Q2 [5]}}