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Expotential - Definition of Exponential Function The...

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Definition of Exponential Function
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The function f defined by where b > 0, b 1, and the exponent x is any real number, is called an exponential function. Again, note that the variable x is in the exponent as opposed to the base when we are dealing with an exponential functions. Also note that in this definition, the base b is restricted to being a positive number other than 1. Exponent Key on Calculator
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Before we get going with the actual exponential functions, I wanted to make sure that everyone knew how to use the exponent key on their calculator. Since there are a lot of different calculators I will be go over the more common ones. At this point you need to check to make sure that you know how to use your exponent key, because we will be using it heavily throughout this as well as the next unit. The two main exponent keys found on calculators are (you will only have one of these): Caret top key: ^ Base raised to an exponent key: OR Check to see if you have one of the two main type of exponent keys (you won’t have both). If you don’t have one check the other. If you don’t see either, look in the reference manual that came with the calculator to see which key it is. The caret top key is most frequently found on graphing calculators but can be found on other types of calculators. On most graphing calculators your exponent key is the caret top key: ^. If you have the caret top key let's practice taking 15 and raising it to the 5th power. To do this you would type in 15^5 and press your enter or = key. If you got 759375, you entered it in correctly. If not, try again. If you still can't get it look in your reference manual that came with the calculator. The key that look like OR are most common in business and scientific calculators, but can be found on other types of calculators. On most business and scientific calculators, the exponent key looks like or or very similar to this . If you have this key let's practice taking 15 and raising it to the 5th power. In this situation, you first type in your base then you activate your exponent key and then you type in your exponent and then press enter or equal. Go ahead and try it out by finding 15 raised to the 5th power. Type in 15, then press or and then type in 5 and press the enter or equal key. You should have gotten 759375 as your answer. If not, try again. If you still can't get it look in your reference manual that came with the calculator.
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Base e e is approximately 2.718281828... The exponential function with base e is called the natural exponential function . e has a value attached it (similar to pi). e is approximately 2.718281828... This base is used in economic analysis and problems involving natural growth and decay. At this point, we are just going to learn how to find the value of e raised to an exponent using the calculator.
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