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#### Overview of this book

Are you looking to start developing artificial intelligence applications? Do you need a refresher on key mathematical concepts? Full of engaging practical exercises, The Statistics and Calculus with Python Workshop will show you how to apply your understanding of advanced mathematics in the context of Python. The book begins by giving you a high-level overview of the libraries you'll use while performing statistics with Python. As you progress, you'll perform various mathematical tasks using the Python programming language, such as solving algebraic functions with Python starting with basic functions, and then working through transformations and solving equations. Later chapters in the book will cover statistics and calculus concepts and how to use them to solve problems and gain useful insights. Finally, you'll study differential equations with an emphasis on numerical methods and learn about algorithms that directly calculate values of functions. By the end of this book, you’ll have learned how to apply essential statistics and calculus concepts to develop robust Python applications that solve business challenges.
Preface
1. Fundamentals of Python
Free Chapter
2. Python's Main Tools for Statistics
3. Python's Statistical Toolbox
4. Functions and Algebra with Python
5. More Mathematics with Python
6. Matrices and Markov Chains with Python
7. Doing Basic Statistics with Python
8. Foundational Probability Concepts and Their Applications
9. Intermediate Statistics with Python
10. Foundational Calculus with Python
11. More Calculus with Python
12. Intermediate Calculus with Python

Much like population problems, half-life problems concern a population, but one of atoms of radioactive materials where half the atoms change over time into atoms of a different substance. For example, Carbon-14 decays into Nitrogen-14, and it takes about 5,730 years for half the carbon to decay. This makes radiocarbon dating a crucial tool in everything from archaeology to detecting forged artworks.

## Exercise 12.08: Measuring Radioactive Decay

Radium-226 has a half-life of 1,600 years. How much of the radium in a given sample will disappear in 800 years?

The differential equation meaning "the rate of decay of a substance is proportional to the amount of the substance" is expressed like this:

Figure 12.10: Differential equation for calculating rate of decay of a substance

The solution is similar to that for our population problems, except that the decay factor is negative, since the amount decreases:

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