One method to determine the time since an animal died is to estimate the percent

Question

One method to determine the time since an animal died is to estimate the percentage of carbon -14 remaining in is bones. The percent P in decimal form of carbon-14 remaining x years is given by P(x) = e^-0.000121x. Approximate (to the nearest whole year) the age of a fossil if there is 54% ofcarbon-14 remaining. In the formula A(t) = A0e^Kt, A is the amount of radioactive material remaining from an initial amount A0 at a given time t, and k is a negative constant determined by the nature of the material. A certain radioactive isotope decays at a rate of 0.1% annually Determine the half-life of this Isotope, to the nearest year. Use the formula M = log (l/l0), where the magnitude of an earthquake on the Richter scale is based on I, the measurement of a seismic wave and I0. the measurement of a seismic wave of a level zero earthquake with the same epicenter. If an earthquake measured 6.3 on the Richter scale, what was the intensity of the earthquake? Round to the nearest whole number. How long must $5100 be in a bank at 5% compounded annually to become $9616.81?

Explanation / Answer

71: Given that 0.54 fraction of carbon - 14 is remaining. Hence

0.54 = (exp)-0.000121x

=> ln(0.54) = - 0.000121x

=> x = ln(0.54) / (-0.000121) = 5092 years

=> x = 5092 years

Hence approximate age of the fossil is 5092 years.

72: Given when t = 1 year, A(t) = 0.999A0

Now applying the formulae

A(t) = A0x(exp)^kt

=> 0.999A0 = A0 (exp)^kx1 yr

=> (exp)^kx1yr = 0.999

=> kx1yr = ln0.999

=> k = ln(0.999) / 1 yr = - 0.00100 yr-1

For first order reaction

half-life, t1/2 = 0.693 / k = 0.693 / 0.00100 yr-1 = 693 year (answer)

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