SOLUTION: A piece of charcoal is found to contain 39​% of the element B that it originally had. ​(a) When did the tree from which the charcoal came​ die? Use 5800 years as the​ half

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: A piece of charcoal is found to contain 39​% of the element B that it originally had. ​(a) When did the tree from which the charcoal came​ die? Use 5800 years as the​ half      Log On


   

Question 1157061: A piece of charcoal is found to contain 39​% of the element B that it originally had.
​(a) When did the tree from which the charcoal came​ die? Use 5800 years as the​ half-life of the element B.
​(b) Using a graphing​ utility, graph the relation between the percentage of the element B remaining and time.
​(c) Using​ INTERSECT, determine the time that elapses until half of the the element B remains.
​(d) Verify the answer found in part ​(a).
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A piece of charcoal is found to contain 39​% of the element B that it originally had.
Use the radioactive decay formula: A = Ao*2^(-t/h), where
A = resulting amt after t time
Ao = initial amt
t = time of decay
h = half life of substance
:
​(a) When did the tree from which the charcoal came​ die?
Use 5800 years as the​ half-life of the element B.
Assuming initial amt is 1
2^(-t/5800) = .39
-t%2F5800ln(2) = ln(.39)
-t%2F5800= ln%28.39%29%2Fln%282%29
-t%2F5800 = -1.35845
t = -5800 * -1.3845
t = 7879 yrs
:
​(b) Using a graphing​ utility, graph the relation between the percentage of the
element B remaining and time.
the equation for this: y = 100*2^(-x/5800)
+graph%28+300%2C+200%2C+-2000%2C+15000%2C+-20%2C+105%2C+100%2A2%5E%28-x%2F5800%29%2C+50%29+
:
​(c) Using​ INTERSECT, determine the time that elapses until half of the the
element B remains. Did that
:
​(d) Verify the answer found in part ​(a). confirmed, entered 7879 and got 39