Answer to Question #97467 in Algebra for kiley

Question

A scientist begins with 250 grams of a radioactive substance. After 250 minutes, the sample has decayed to 16 grams. Write an exponential equation
f(t)
representing this situation. (Let f be the amount of radioactive substance in grams and t be the time in minutes.)
To the nearest minute what is the half life?

Answer 1

$f(t)=250e^{-kt}$

After 250 min: $16=250e^{-250k}$

So, $k=\frac{ln250-ln16}{250}=0.011$

To find the half life we should solve: $0.5=e^{-0.011t}$

Thus the half life: $t=\frac{ln0.5}{-0.11}=63 \;min.$