Radiocarbon dating is a method used by scientists to estimate the age of ancient objects that were once living matter, such as bone, leather, wood, or paper. Allof these contain carbon, a proportion of which is carbon-14,a radioactive isotope that is continuouslybeing formed in the upper atmosphere. Since livingorganisms take up radioactive carbon along with othercarbon atoms, the ratio between the two forms remainsconstant. However, when an organism dies,the carbon-14 in its cells decays and is not replaced.Carbon-14 has a known half-life of 5730 years, so bymeasuring the concentration of carbon-14 in anobject, scientists can determine its approximate age.One of the most successful applications of radiocarbondating has been to determine the age of theStonehenge monument in England (Figure 6.25).Samples taken from the remains of wooden posts werefound to have a concentration of carbon-14 that was45% of that found in living material. What is theestimated age of these posts?
MTH 132 - Lecture 26 - Newtonian method Roots ● Frequently, there are issues when we attempt to solve “imperfect” equations, where the roots result in imaginary numbers or no neat solution - we have to resort to an approximation. ● Newton’s method is essentially a way to approximate by narrowing down the numbers until they reach a specific accuracy that you specify. How does this work ● The concept of the IVT or intermediate value theorem guarantees the Newtonian method. Intermediate Value Theorem - Which Intervals are continuous ● If f(x) is continuous on the closed interval on [a,b] and c is between a and b; then there exists a point (d) on the interval [a,b] such that f(d) = c. Application of IVT: ● Prove the existence of a solution. ● f(x) = g(x) on [a,b] ● Step 1: h(x) = f(x) - g(x) ● Check if h(x) is continuous on [a,b] ●
