Radioatividade e datação por carbono-14: uma proposta didática para o ensino da função exponencial

Abstract

The applications of differential equations span various fields of research, including physics, chemistry, biology, and many others that involve modeling and solving problems with conditions that vary over time. In this context, the aim of this dissertation is to study the solution of first-order ordinary differential equations (ODEs) involving exponential functions and to relate the teaching of this concept to high school students. To achieve this, the study is based on the dating method using the radioactive decay of carbon-14, where the solution of the ODE plays a key role. Thus, the research explores the history and definition of the atom, atomic models, and the applications and consequences of radioactivity, culminating in the dating of a human fossil discovered over 30 years ago, known as “Ötzi, the Iceman.” From this foundation, a teaching proposal is developed, applying the exponential function to an interdisciplinary project inspired by the case of “Ötzi”. Each discipline involved in the project will explore a line of interest. In mathematics, an experimental activity is proposed to illustrate the probabilistic nature of atomic decay, along with the construction of a graph of the related exponential function. Additionally, a problem-solving activity is included to determine the age of the fossil and the amount of carbon-14 present at the time of its dating using an exponential function. The educational product, structured as a teaching model, was presented as an experiment without student participation but has the potential to be implemented in classroom teaching practices.