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Decay Problem A zircon sample contains 4000 atoms of the radioactive element 235U. Given that 235U has a half-life of 700 million years, how long would it take to decay to 125 atoms? Solve the equation via MATLAB making sure that you passed though the following: 1. Initialization of variables 2. Setting up the differential equations 3. Listing down initial Conditions Script 4. Solving for the parameter k 5. Finding the resulting model 6. Finding the period where the amount will be 125 atoms 7 Graph the solutions 1 %A zircon sample contains 5000 atoms of the radioactive element 2350. 2 %Given that 235U has a half- life of 650 million years, how long would it take to decay to 120 atoms? 3 Save 4 %Setup the variables A(t), k that will be used in the program. Find also the derivative of A(t) and set as dA 5 syms 6 dA 7 8 %Initial Conditions 9 condi- 10 cond2- 11 Acondition 12 13 %Set the differential equation model as eqn1; 14 eqn1 15. 16 %Find k1 and k2, by solving the initial value problem eqni using condi and cond2, respectively. 17 k1- 18 K2- 19 28 %Solve for k by equating ki and k2 at t-8. Save results as k. 21 22 23 %Solve the eqni using the acquired value of k and using Initial value cond1. 24 25 26 %Solve the equation when A(t) = Acondition. Save Answer as tfinal (This is in Million Years) 27 28 29 %Express your answer in years 30 40 41 42 43 C Reset 31 32 33% Plot the equation: Use the Title-Radioactive Decay, XValue-Period (Million of Years), Walue-Atoms of 235U 34 35 36 37 %Use the domain (0, tfinal+5) with 0.2 gaps from each point 38 x=0:0.2:tfinal+500; y-Asoln(x); 44 45 My Solutions > MATLAB Documentation ▶ Run Script ?