Half life of a certain radioactive material is 130 days. After what lapse of time, the undecayed fraction of the material will be 25% ?

Explanation

Half time = `T_(1//2)=130` days
`t=?`
`(N)/(N_(0))=25%=(25)/(100)=(1)/(4)`
`(N)/(N_(0))=((1)/(2))^(t//T_(1//2))`
`(1)/(2)=((1)/(2))^(t//130)`
`((1)/(2))^(2)=((1)/(2))^(t//130)`
`implies 2=(t)/(130)`
`implies t=2xx130=260` days