Raymond B. answered • 01/19/22
Math, microeconomics or criminal justice
if the half life is 710 years, then 20 grams will decay to 10 grams in 710 years. In 100, a rough guess is maybe 18 grams will be left. 100 is a little less than 1/7 of 710. 1/7 x 1/2 = 1/14. 13/14 of 20 might be left. 13/14 x 20 = about 18.6 This is not accurate, but a very rough estimate, a linear extrapolation, when the variables are not linearly related.
10 = 20e^710r
1/2 = e^710r
ln(1/2) = 710r
r = ln.5/710 = about -.0009762636
A = 20e^100(-.00097626) = (20)(1/1.102550354)
= 20(.906988)
A = 20 x .906988 = 18.139761 grams or about 18.14 grams
18.1 grams will be left after 100 years
710 is a half life
1420 is a 1/2 x 1/2 =quarter life
355 = 1/sqr2 life = 1/1.414 = a 0.7072135 life
177.5 = 1/(4th root of 2) life = 1/1.1892 life
88,8 = 1/8th root of 2 life= 1/1.090508 = .9170040 life
20 x .917004 = 18.34 grams after 90 years
after 100 years, a little less than 18.34 left such as 18.13 grams
