Algebraically find a function that models the half-life of radium-226.

Question

Consider a 10 gram sample of radium-226 whose half-life is about 1600 years.

 

Algebraically find a function that models the half-life of radium-226.

Answer 1

I think what you really want is a function that models the mass of radium-226 as a function of time, given a half-life of 1600 years.  This is an exponential decay problem.

 

M₀ = initial mass of radium-226 = 10 g

t = elapsed time in years

M(t) = mass remaining after time t, in grams

 

M(t) = M₀ (1/2)^t/1600

 

M(t) = 10 (1/2)^t/1600