In this section, we explore some important applications in more depth, including radioactive isotopes and Newton’s Law of Cooling.

In real-world applications, we need to model the behavior of a function.

The task requires the student to use logarithms to solve an exponential equation in the realistic context of carbon dating, important in archaeology and geology, among other places.

carbon dating and logarithms-64

Radiocarbon dating was discovered in 1949 by Willard Libby, who won a Nobel Prize for his discovery.

It compares the difference between the ratio of two isotopes of carbon in an organic artifact or fossil to the ratio of those two isotopes in the air.

Exponential growth and decay graphs have a distinctive shape, as we can see in [link] and [link].

It is important to remember that, although parts of each of the two graphs seem to lie on the -axis.

It is believed to be accurate to within about 1% error for plants or animals that died within the last 60,000 years.

Carbon-14 is a radioactive isotope of carbon that has a half-life of 5,730 years.

Expressed in scientific notation, this is We now turn to exponential decay.

One of the common terms associated with exponential decay, as stated above, is half-life, the length of time it takes an exponentially decaying quantity to decrease to half its original amount.

We use half-life in applications involving radioactive isotopes.