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?