What does it mean for something to change exponentially? Let's learn about a new family of functions, and use these exponential functions to analyze real-world scenarios.

While both involve exponential functions, exponential growth refers to when the quantity is increasing over time, while exponential decay refers to when the quantity is decreasing over time.

Here's a sneak preview – don't worry if you don't understand all of it yet: We'll explore exponential growth and logistic growth in more detail below.

In this unit, we learn how to construct, analyze, graph, and interpret basic exponential functions of the form f (x)=a⋅bˣ.

It tells you that the graph is for the function named "f" that accepts input values of "x". If you have an equation that is a function, the "y" in the equation is replaced with f (x).

In this video, I want to introduce you to the idea of an exponential function and really just show you how fast these things can grow. So let's just write an example exponential function here.

Not exactly, but they are similar in nature. It's just that geometric sequences deal with discrete variables whereas exponential functions deal with continuous ones.

Linear growth is constant. Exponential growth is proportional to the current value that is growing, so the larger the value is, the faster it grows. Logarithmic growth is the opposite of exponential growth, it …

For exponential functions, the basic parent function is y=2^x which has a asymptote at x=0, but if it is shifted up or down by adding a constant (y = 2^x + k), the asymptote also shifts to x=k.

Both exponential growth and decay functions involve repeated multiplication by a constant factor. However, the difference lies in the size of that factor: - In an exponential growth function, the factor is …