Summary  
This chapter demonstrates how to define and implement exponential and logarithmic functions in Python using NumPy for computation (np.exp and np.log with a change-of-base formula), generate input values, and visualize the resulting curves with Matplotlib.  

General domain of usage  
Finance

## Exponential Function
Exponential functions model rapid growth or decay, commonly used in population modeling, finance, and physics. This function is of the form $$f(x) = ae^{bx}$$.

### Code Breakdown
- Generates `x` values between `-5` and `5`;
- Defines `exponential_function(x, a, b)`, where `a` scales the function, and `b` controls the growth rate;
- Plots the graph with **arrows** at both ends to show continuous growth;
- Marks the **y-intercept** at `x = 0` for clarity.


## Logarithmic Function

Logarithms are the inverse of exponentials, useful in scaling data and measuring natural growth processes. This function is defined as $$f(x) = \log_2(x)$$, meaning it calculates the power to which $$2$$ must be raised to obtain $$x$$.

### Code Breakdown
- Generates `x` values between `0.1` and `10` (to avoid `log(0)`, which is undefined);
- Defines `logarithmic_function(x, base=2)`, ensuring base `2` is used throughout;
- The graph includes an **arrow at the right end**, indicating it continues indefinitely;
- The **x-intercept** is marked at `x = 1`, where `log_2(1) = 0`.


Which base is used in the logarithmic function in this code?

Master the mathematical foundations essential for data science. Explore core concepts in functions, calculus, linear algebra, probability, and dimensionality reduction. Build both theoretical understanding and practical coding experience to strengthen your ability to analyze data, model complex systems, and apply advanced techniques in machine learning.

Explore the foundation of mathematical functions. Learn different types of algebraic and transcendental functions, their properties, and how to implement them in Python to solve real-world problems.

Master the concepts of sets and series, from basic operations to practical applications. Gain hands-on experience implementing set operations and working with arithmetic and geometric series in Python.

Develop a solid understanding of limits, derivatives, integrals, and partial derivatives. Connect theory to practice by implementing these concepts in Python and applying them to optimization through gradient descent.

Build strong knowledge of vectors, matrices, and transformations. Learn decomposition methods and eigenvalue analysis, while reinforcing concepts with Python coding challenges and practical data science applications.

Dive into probability theory and statistics. Study conditional probability, Bayes' theorem, and statistical measures. Implement key concepts in Python, simulate distributions, and strengthen your skills through challenges and quizzes.

Implementing Exponential-Log Functions in Python

Exponential Function

Code Breakdown

Logarithmic Function

Code Breakdown

Awesome!

Implementing Exponential-Log Functions in Python

Exponential Function

Code Breakdown

Logarithmic Function

Code Breakdown