# Radioactive radium has a half-life of approximately 1599 years. What percent of a given amount remains after 100 years?

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Expert Answers

mathace | Certified Educator

Formula: `y=Ce^(kt)` where y is the amount of radioactive radium at time t, k is the decay constant, and C is the initial amount of radium

`1/2C=Ce^(k*1599)`

`1/2=e^(k*1599)`

`ln(1/2)=1599klne`

`ln(1/2)=1599k`

`ln(1/2)/1599=k`

`k=-4.3349x10^-4`

`y=Ce^(kt)`

`y=Ce^[(-4.3349x10^-4)(100)]`

`y=.9576C`

**Final Answer: 95.76%** of radioactive radium is left after 100 years.