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AVprozaik [17]
3 years ago
12

Radioactive Decay

Mathematics
1 answer:
Serhud [2]3 years ago
4 0

Answer:

t=160.82 years

Step-by-step explanation:

exponential decay function is

A= A_1 e^{kt}

If initial amount A_1 is 100 then material remaining is 99.57

99.57=100e^{kt}

divide both sides by 100, question says 1 year so t=1

.9957=e^{k(1)}

take ln on both sides

ln(.9957)=k

k=-.00431  

A=100e^{-.00431t}

t=1, A= 50 remaining (half life)

50=100e^{-.00431(t)}

divide both sides by 100

0.5=e^{-.00431t}

take ln on both sides

t=160.82 years

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