Are exponential equations the same as exponential functions?

I am writing a summary of this year's Pre-Calculus lessons and one of the topics on the outline is "Exponential Equations", but on the lesson Power Points on my teacher's website there is only one labeled "Exponential Functions", are they the same thing?

An equation is not a function. However, the definition of a function is usually written as an equation, as in

f(x) = 2e^x - 7

But, that's really just a definition. An equation is usually something you have to solve for a particular value. For example, you might have to solve the equation

e^x - 7x = 12sin(2x)

if you want to find some particular values of x which make the equation true. The above equation must be solved numerically or graphically, as at

http://www.wolframalpha.com/input/?i=solve+e^x+-+7x+%3D+12sin%282x%29

Exponential equations and exponential functions are closely related, but they are not exactly the same thing.

In mathematics, an exponential equation is an equation in which one or both sides involve exponential terms. These equations involve variables appearing as exponents, such as the equation 2^x = 16. The goal in solving an exponential equation is to find the value(s) of the variable that make the equation true.

On the other hand, an exponential function is a specific type of mathematical function that can be represented by the form f(x) = a^(bx), where "a" and "b" are constants and "x" is the variable. Exponential functions have a constant base raised to a variable power. These functions are commonly used to model situations like population growth, compound interest, radioactive decay, and more.

Now, in the context of your Pre-Calculus lessons, it's possible that your teacher used the term "exponential functions" to refer to both the concept of exponential equations and the associated functions. Sometimes, teachers use the term "exponential functions" as a broader umbrella term to cover both concepts. However, to be sure about the specific topics covered in your course, it would be best to consult your teacher directly or refer to your course materials.

When writing your summary, you can mention that exponential equations and exponential functions are related concepts within mathematics. It could also be helpful to include examples of both exponential equations and exponential functions to provide a clearer understanding of each concept.