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January 30, 2015

January 30, 2015

Posted by **j** on Friday, July 24, 2009 at 1:11pm.

1. Find the rate of change of an initial amount of 1 gm of carbon-14 found in the scrolls, if the decay constant is given as λ = 1.21 x 10-4.

2. If the percentage of carbon-14 atoms remaining in a sample is 79%, how old is the sample?

- calculus -
**MathMate**, Saturday, July 25, 2009 at 9:00am1.

dN/dt = -λN

so the initial rate of change

= -1.21*10^4 × 1 g/year

= -0.000121 g/year

2.

N = N_{0}e^{-λt}

e-λt = N/N_{0}

taking logs on both sides

-λt = ln(N/N_{0})

t = -ln(N/N_{0})/λ (before present, year 1950)

= -ln(0.79)/(1.21*10^{4}) (BP)

= 1948 (BP)

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