Homework Help Forum: calculus

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

Carbon-14 is a radioactive substance produced in the Earth's atmosphere and then absorbed by plants and animals on the surface of the earth. It has a half-life (the time it takes for half the amount of a sample to decay) of approximately 5730 years. Using this known piece of information, scientists can date objects such as the Dead Sea Scrolls. The function N = N0e-λt represents the exponential decay of a radioactive substance. N is the amount remaining after time t in years, N0 is the initial amount of the substance and λ is the decay constant. 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 9:00am

  1. dN/dt = -λN so the initial rate of change = -1.21*10^4 × 1 g/year = -0.000121 g/year 2. N = N0e-λt e-λt = N/N0 taking logs on both sides -λt = ln(N/N0) t = -ln(N/N0)/λ (before present, year 1950) = -ln(0.79)/(1.21*104) (BP) = 1948 (BP)

  
  

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