Please help me solve this half-life word problem

Question

The half-life of a radioactive substance is 2,500 years. If 20 grams are present now, how much will be present in 50 years? (Round your answer to two decimal places.)

Answer 1

Zandalee, (interesting name)

 

    We usually model radioactive decay with an exponential model A(t)=A₀*e^-kt where A₀ is  the amount present at t=0 and k is a constant. The half-life is the time it takes for an initial amount to defy to 1/2 it's initial value.

 

So at t=2500 yrs A(2500)=A₀ /2 so 1/2=e^-k*2500 , taking the natural logs of both sides gives

 

-.693=-k*2500 solving for k gives k= .693/2500

 

In 50 years 20 grams will decay to 20*e^{-.693*50/2500}  =19.92 grams.

 

Jim