Question 1199238
The half-life of Radium 266 is 1590 years
 how many years does it take for 100mg of Radium 266 to decay to a mass of 70mg?
:
The radioactive decay formula: 
A = Ao*2^(-t/h), where:
A = resulting amt after t years
Ao = initial amt
t = time of decay
h = half-life of substance
:
In this problem we can write it
100*2^(-t/1590) = 70 
2^(-t/1590) = {{{70/100}}}
2^(-t/1590) = .7
using nat logs{{{(-t/1590)*ln(2) = ln(.7)}}}
ln(2^(-7/1590)) = ln(.7)
log equiv of exponents
{{{(-t/1590)*ln(2) = ln(.7)}}}
{{{(-t/1590)}}} = {{{ln(.7)/ln(2)}}}
calc
{{{-t/1590}}} = -.51457
t = -1590 * -.51457 
t = 818 years