Question: This is on the application of first-order differential equations, specifically targeting: radioactive decay / biological growth. Radium was found to decompose 2% of its initial

This is on the application of first-order differential equations, specifically targeting: radioactive decay / biological growth.

Radium was found to decompose 2% of its initial quantity after 20 years. Determine the half-life of the radioactive substance.

a. What is the working equation for this problem? b. What is the general solution for the given radioactive substance? c. What is the boundary condition to determine the constant C. d. After 20 years, what is the remaining quantity of the radioactive substance with reference to its initial amount? e. What is the boundary condition to compute for the proportionality constant k? f. What is the particular equation for the given radioactive substance? g. What is the half-life of the radium in years?

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