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Welcome to our Math lesson on What are Exponential Functions?, this is the first lesson of our suite of math lessons covering the topic of Exponential Graphs, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
In tutorial 7.1 and tutorial 13.2 we explained the meaning of the term 'exponent', which indicates the number of equal factors multiplied by each other in a recurring multiplication. For example, in the expression 24 = 16, the number 4 is the exponent, which shows how many equal factors (this common factor is called 'base' and in this specific case, the base is 2) multiply with each other to give the result, which we call 'power'.
The term 'exponential' derives from 'exponents', which we also call 'indices'. We have seen in tutorial 13.2 that exponential equations are those equations which have the variable in the exponent. Similarly, exponential functions are those functions that have the independent variable written as an index (exponent). The simplest form of exponential functions is
where a is a known number called the base. Recall the notation y(x), which is exclusively used in functions theory to indicate the dependent variable y in terms of the independent variable x but you can ignore it and write simply y instead of y(x).
However, the general form of an exponential function includes more terms than above. It contains a first-degree monomial in the exponent and a coefficient preceding the base a that multiplies the expression on the right side. Therefore, the general form of an exponential function is
It is clear that in the simplest form of exponential functions y = ax we have k = 1, m = 1 and t = 0.
Find the values of a, k, m and t in the exponential function
This function is not actually expressed in the standard form
so, the first thing to do is to transform it into the standard form. Thus, we write
Comparing the last expression with the standard form of the exponential function we obtain the following values:
You have reached the end of Math lesson 15.5.1 What are Exponential Functions?. There are 8 lessons in this physics tutorial covering Exponential Graphs, you can access all the lessons from this tutorial below.
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