Experiments show that radius disintegrates at a rate proportional to the amount of radium present at the moment. Its half life is 1590 years. What percentage will disappear in one year? [Use `e^(-log2/1590)=0. 9996`]

Explanation

Given,

`(dA)/(dt)=-kA`

`(dA)/A=(-kdt)`

`logA=-ktr+c->(1)`

now at `t=0,A=A_0`

So,

`log|A_0|=0+c`

`log|A_0|=c->(2)`

...