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Unformatted text preview: Now, divide by 5730 to solve for k. k = ln (1/2) . /. 5730 = -1.21e-4 Now that we know the value of k, we insert 99.5% into the equation to find out how many years it takes for the pictures carbon-14 to decay 99.5%. .995 = e (-1.21e-4)t Again, we need to take the ln of both sides to get ride of e. ln (.995) = (-1.21e-4 )t Divide by -1.21e-4 to solve for t, time in years. t = ln (.995) . /. -1.21e-4 = 41.426 We concluded that the picture is fake. We know this because it only takes 41.426 years for the carbon-14 to decay to 99.5%, but they claim it is over 300 years old. If it were truly over 300 years old, there would be much less carbon-14 present....
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- Fall '08