SOLUTION: Half-life. Exercise gives a half-life for an exponentially decaying quantity. 22. The half-life of a radioactive substance is 250 years. If you start with some amount of this su

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Half-life. Exercise gives a half-life for an exponentially decaying quantity. 22. The half-life of a radioactive substance is 250 years. If you start with some amount of this su      Log On


   

Question 112028This question is from textbook Essentials of using and understanding mathematics
: Half-life. Exercise gives a half-life for an exponentially decaying quantity.
22. The half-life of a radioactive substance is 250 years. If you start with some amount of this substance, what fraction will remain in 70 years? In 1500 years? This question is from textbook Essentials of using and understanding mathematics

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Half-life. Exercise gives a half-life for an exponentially decaying quantity.
22. The half-life of a radioactive substance is 250 years. If you start with some amount of this substance, what fraction will remain in 70 years?
:
The half-life formula:
A = Ao(2^(-t/h))
where
A = resulting amt
Ao = initial amt
t = time (in yrs in this case)
h = half-life of the substance
:
Since they want this in a fraction, start with Ao = 1
t = 70 yrs
h = 250 yrs
:
Substitute and we have:
A = 1[2^(-70/250)]
A = 2^-.28
Find the value of 2^-.28 on a good calc
A = .8236
We can say 8236%2F10000 is left or 82.36% of the initial material remains
:
:
In 1500 years?
Same, except substitute 1500 for t
A = 1[2^(-1500/250)]
A = 2^-6
A = .015625 or about 1.56% remains after 1500 years