SOLUTION: Can you please help me solve this word problem? Radium has a half-life of 1660 years. If the initial amount of radium is 200 grams, how much will remain in 500 years? I was s

Question 136965This question is from textbook Algebra 2 and Trigonometry
: Can you please help me solve this word problem?
Radium has a half-life of 1660 years. If the initial amount of radium is 200 grams, how much will remain in 500 years?
I was so lost on this problem and any help would be greatly appreciated.
Thanks! This question is from textbook Algebra 2 and Trigonometry

Found 2 solutions by ankor@dixie-net.com, scott8148:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Radium has a half-life of 1660 years. If the initial amount of radium is 200 grams, how much will remain in 500 years?
:
Just use the half-life equation which is:
:

Where:
A = remaining amt
Ao = initial amt
t = time
h = half-life of the given substance
:
Substituting the given values we have:
:

:
A = 200 * .81157; find that 2^(-500/1660) = .81157 on a good calc
:
A = 162.3 gr left after 500 yrs
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
the amount remaining (A) is equal to the initial amount (I) reduced by the number of half-lives that have elapsed
__ (1/2)^(t/h), where t is the time and h is the length of a half-life

A=I(1/2)^(t/h) __ A=200(1/2)^(500/1660)
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