Differential Equations MATH 2320 FINAL EXAM Show all work or reasoning in the sp

Question

Differential Equations MATH 2320 FINAL EXAM Show all work or reasoning in the space given and/or on the back of the exam to receive full credit. Do not turn in any separate paper. 1. Radioactive element W decays to element X with decay constant 0.3. Element X decays to element Y with decay constant of 0.7. Element Y decays to stable element Z with decay constant of 0.4. Write down the system of differential equations for the amounts, w,) y(), and z() of the elements W, X, Y, and Z, respectively, at time t. If, initially, there are 15 grams of X, but no Y or Z, solve the system using separable and/or linear methods

Explanation / Answer

dW/dt = - 0.3W,
dX/dt = 0.3 W - 0.7 *X,
dY/dt = 0.7 X - 0.4*Y,
dZ/dt = 0.4 Y

X(0) = 15 ,Y(0) = 0 , Z (0) = 0

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