3. Consider a nuclear reactor operating with a constant power of 0.5MWt. From t=0, the reactivity was changed as given in the following figure : p(reactivity) 0.1$ 0 10 50 Assume that the delayed neutron fraction (B) is 0.0065. Also, use the following simplified point kinetic equation with one-group effective delayed neutrons to calculate the reactor power change as time : dP _ p(t) _p(t) + C(t), dt A dC = B_P(t)-AC(t); B = 0.0065; 2=0.08 sec; A = 10- sec dt A 70 = @[A + Please answer the following questions : (a) Estimate the reactor power change as time using the backward difference scheme. Please discretize the time interval (0~70sec) into 100 steps. Plot the power change. @+2 t(sec) (b) Estimate the reactor power change as time using the Hansen's method. Please discretize the time interval (0~70sec) into 100 steps. Plot the power change. The inhour equation for the simplified point kinetic equation is given by p=@A+ w @ +2 ]. You can use any program language (e.g., Phython, Fortran, C (C++), Mathlab,...). (c) Try to estimate the reactivity change using Eq.(21)~(24) and using the power change you obtained in (b). Did you get the same values given in the figure? 1/2