+466 This decay was exponential. After 10 minutes there were 480, but after 40 minutes only 470 remained. What was the half-life of the things?
This decay was exponential. After 10 minutes there were 480, but after 40 minutes only 470 remained. What was the half-life of the things?
40 - 10 =30 time elapsed
470/480=.9791667 remains after 30 minutes
.9791667Ao=Ao. e^(30k), where k=constant
k=ln(.9791667) / 30
k=-7.0178e-4
1/2Ao=Ao . e^(-.00070178t)
t=ln(1/2) / (-.00070178)
t=987.70 minutes- half-life of the radioactive substance.
Let half-life =t
47/48 = 2^(-30/t)
47/48 = 2^(-30/t) is equivalent to 2^(-30/t) = 47/48:
2^(-30/t) = 47/48
Take reciporicals of both sides:
2^(30/t) = 48/47
Take the logarithm base 2 of both sides:
30/t = (log(48/47))/(log(2))
Take the reciprocal of both sides:
t/30 = (log(2))/(log(48/47))
Multiply both sides by 30:
Answer: | t = (30 log(2))/(log(48/47))=987.70 minutes-half-life of the element.
