SOLUTION: use a graph to approxiamate the age of rock that has 70% of its original K40. 50%=1.3 billion yrs, 25%=2.6 billion.. thank you

Algebra ->  Graphs -> SOLUTION: use a graph to approxiamate the age of rock that has 70% of its original K40. 50%=1.3 billion yrs, 25%=2.6 billion.. thank you      Log On


   

Question 849667: use a graph to approxiamate the age of rock that has 70% of its original K40. 50%=1.3 billion yrs, 25%=2.6 billion.. thank you
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
use a graph to approximate the age of rock that has 70% of its original K40. 50%=1.3 billion yrs, 25%=2.6 billion..
:
Assign the given data as:
x1 = 50; y1 = 1.3
x2 = 25; y2 = 2.6
Find the slope using m = %28y2-y1%29%2F%28x2-x1%29
m = %282.6-1.3%29%2F%2825-50%29 = -1.3%2F25
Find the equation using the point/slope form; y - y1 = m(x-x1)
y - 1.3 = -1.3%2F25(x - 50)
y - 1.3 = -1.3%2F25x + 2.6
y = -1.3%2F25x + 2.6 + 1.3
y = -1.3%2F25x + 3.9
Graph this equation
+graph%28+300%2C+200%2C+-20%2C+105%2C+-2%2C+5%2C+%28-1.3%2F25%29x+%2B+3.9%29+
putting this graph in my calc, At 70% the age is only .26 billion yrs
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As I walked away from this problem to do some menial labor, it occurred
to me that his may a radioactive decay proble. They gave us the half-life
when they said 50% at 1.3 million yrs
:
solve it that way with 70% remaining using the decay formula using logs
A = Ao*2(-h/t),
where
A = amt remaining after t time, we will say this is .7
Ao = initial amt (t=0), we will call this 1
t = time of decay (billions of yrs here)
h = half-life of substance 1.3 billion years
:
1*2^(-t/1.3) = .7
-t%2F1.3log(2) = log(.7)
-t%2F1.3 = log%28.7%29%2Flog%282%29
-t%2F1.3 = -.51457
t = -1.3 *-.51457
t = +.669 billion yrs
:
Graphing this, Green line represents 70%, x = billions of yrs
+graph%28+300%2C+200%2C+-1%2C+4%2C+-1%2C+1%2C+2%5E%28-x%2F1.3%29%2C+.7%29
:
Would appreciate if you would let me know which is right here. CK