Numerical Methods: Euler to Runge–Kutta · Medium problem

A bacterial colony grows according to $y' = 2y$ (population, in millions), $y(0) = 1$. Euler's method is used to estimate $y(0.5)$ two ways: one step of size $h = \dfrac{1}{2}$, and two steps of size $h = \dfrac{1}{4}$. Since Euler's global error is approximately proportional to $h$ (first order), the Richardson extrapolate $2Y_{h/2} - Y_h$ cancels this leading error term. Compute the extrapolated estimate of $y(0.5)$. Express your answer as a common fraction.