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?
1
Expert's answer
2019-10-29T08:07:07-0400
"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."
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