SOLUTION: A radioactive substance has a decay rate of 1.8% per year. What is its half life? Give your answer correct to 2 decimal places. The radioactive element carbon-14 has a half-life

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Question 590776: A radioactive substance has a decay rate of 1.8% per year. What is its half life? Give your answer correct to 2 decimal places.
The radioactive element carbon-14 has a half-life of 5750 years. The percentage of carbon-14 present in the remains of plants and animals can be used to determine age. How old is a skeleton that has lost 44% of its carbon-14?
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A radioactive substance has a decay rate of 1.8% per year.
What is its half life? Give your answer correct to 2 decimal places.
:
The radioactive decay formula: A = Ao*2^(-t/h), where
A = amt remaining after t time
Ao = initial amt; t-0
t = time of decay
h = half-life of substance
:
let initial amt = 1
then remaining amt = .982
let t = 1 yr
find h
:
1*2^(-1/h} = .982
Use natural logs
ln(2^(-1/h)) = ln(.982)
:
-1%2Fh = ln%28.982%29%2Fln%282%29
use your calc
-1%2Fh = -.0262
-.0262h = -1
h = 1%2F.0262
h ~ 38.17 yrs is the half-life
:
:
The radioactive element carbon-14 has a half-life of 5750 years.
The percentage of carbon-14 present in the remains of plants and animals can be used to determine age.
How old is a skeleton that has lost 44% of its carbon-14?
:
Find the remaining carbon if initial amt = 1: 1-.44 = .66
Find t
1*2^(-t/5750} = .66
Use natural logs
ln(2^(-t/5750)) = ln(.66)
:
-t%2F5750 = ln%28.66%29%2Fln%282%29
use your calc
-t%2F5750 = -.59946
t = -5750 * -.59946
t = +3,447 years