The half life of radium-226 is 1600 years. a. After how many half-lives would 25% of the radium-226 remain.
b. Write a function m(t) that models the mass remaining after years.
c. How much of the sample will remain after 3000 years?
d. After how long will only 15 mg of the sample remain?

Explanation:

a )

half life = 1600 years

50% in 1600 years

25% in next 1600 years

so 25% in total of 3200 years .

b )

disintegration constant = .693 / half life

= .693 / 1600

λ= 4.33 x 10⁻⁴ year⁻¹

m(t) =

m₀ is initial mass , λ =  4.33 x 10⁻⁴ year⁻¹

c )

m(t) after 3000 years , t = 3000

m(t) =

=

= .2725 m₀

percentage of mass remaining = 27.25 %