The​ half-life of radium is 1690 years. If 60 grams are present​ now, how much will be present in 290 ​years? Question content area bottom Part 1

Answer 1

A = Pe^rt where t= 1690, P =60, r= decay percentage, A=amount left after t years

1/2=.5=e^1690r

take natural logs of both sides

ln.5 = 1690r

divide by 1690

r = ln.5/1690 =close to -.00041 = annual decay rate

formula is A=Pe^-.00041t

A=60e^-.00041(290) = 53.3 grams present after 290 years

or

A = 60(1/2)^(290/1690) = 60(1/2)^29/169

A = 53.3 grams after 290 years