SOLUTION: the half-life of a certain radioactive substance is 8 hours. there are 5 grams present initially. which of the following gives best approximation when there will be 1 gram remainin

Algebra ->  Functions -> SOLUTION: the half-life of a certain radioactive substance is 8 hours. there are 5 grams present initially. which of the following gives best approximation when there will be 1 gram remainin      Log On


   

Question 1048723: the half-life of a certain radioactive substance is 8 hours. there are 5 grams present initially. which of the following gives best approximation when there will be 1 gram remaining.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
y=p%2Ae%5E%28-kt%29--------exponential decay model

Need find k. The variable to find, AFTER k is found, will be t.

HALF LIFE
p%2F2=p%2Ae%5E%28-k%2A8%29
%281%2F2%29=e%5E%28-8k%29
ln%281%2F2%29=ln%28e%5E%28-8k%29%29
-8k%2Aln%28e%29=ln%281%2F2%29
-8k=-ln%282%29
highlight_green%28k=ln%282%29%2F8%29
-
You would like to put a decimal number to that.
k=0.08664, but remember to include the negative sign in the model!!

WHEN THE 5 GRAMS BECOME 1 GRAM? FIND t.
ln%28y%29=ln%28p%2Ae%5E%28-kt%29%29
ln%28p%29-kt=ln%28y%29
-kt=ln%28y%29-ln%28p%29
-kt=ln%28y%2Fp%29
t=%28-1%2Fk%29ln%28y%2Fp%29
highlight%28t=%281%2Fk%29ln%28p%2Fy%29%29, if you want to keep the positive value of k found earlier.

YOU FINISH IT.
system%28p=5%2Cy=1%2Ck=0.08664%2Ct=YouNeedToEvaluateHours%29