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\fConsider the ODE dy/de = f(x, y), with y(0) = 0. Suppose that the second order Runge Kutta method is used to obtain the solution for y(x = 1), dividing the interval into N subintervals. Suppose that N is large and consider the error on y( = 1). By what factor does this error decrease when N is increased by a factor of 10? [ Recall that the 2nd order Runge Kutta method evaluates yit1 = yi + k2 + O((8x)), where k2 = ox f(x,, y:), k2 - 6x f(x; + 6x/2, y: + k1/2) ]. O 10000 100 10 1000Question 12 10 p Radioactive nuclei decay at the rate R, measured in seconds, i.e. dN/dt = -RN. What fraction of an initial population of nuclei remains after time t = 5R? Oe-5 O 1/5 O (1/2)5 Next\f