SOLUTION: An accident in 1986 at the Chernobyl nuclear plant in Ukraine released a large amount of plutonium (Pu-239) into the atmosphere. The half-life of Pu-239 is about 24,110 years. Find

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: An accident in 1986 at the Chernobyl nuclear plant in Ukraine released a large amount of plutonium (Pu-239) into the atmosphere. The half-life of Pu-239 is about 24,110 years. Find      Log On


   

Question 1115542: An accident in 1986 at the Chernobyl nuclear plant in Ukraine released a large amount of plutonium (Pu-239) into the atmosphere. The half-life of Pu-239 is about 24,110 years. Find the decay constant. Use the function N(t)=Noe^-kt to find what remains of an initial 20 grams of Pu-239 after 5000 years. How long will it take for these 20 grams to decay to 1 gram?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
N(t)=Noe^-kt

Do it this way in pure text
N(t)=N[o]e^(-kt)
N%28t%29=N%5Bo%5De%5E%28-kt%29

Reassigning variables for typewriting convenience:
N=ne%5E%28-kt%29, N for function and n for initial quantity

ln%28N%29=ln%28ne%5E%28-kt%29%29
ln%28N%29=ln%28n%29%2B%28-kt%29%2A1
-kt%2Bln%28n%29=ln%28N%29
-kt=ln%28N%29-ln%28n%29
kt=ln%28n%29-ln%28N%29
k=%28ln%28n%29-ln%28N%29%29%2Ft

You were given half-life is 24110 years. This means ln%28n%2FN%29=ln%281%2F%281%2F2%29%29=ln%282%29;
highlight%28k=ln%282%29%2Ft%29
and
k=ln%282%29%2F24110
highlight%28k=0.00002875%29

The original model, highlight_green%28highlight%28N%28t%29=N%5Bo%5De%5E%28-0.00002875t%29%29%29