Study GuidePrecalculus–Exponential and Logarithmic Functions1.Exponential FunctionsAnexponential functionhas the form:where the base (a) is apositive real number((a > 0)).Key ideas to remember:•Theinput(the domain) can beany real number.•Theoutput(the range) is alwayspositive.•Exponential functions grow or decay very quickly compared to linear functions.The Natural Exponential FunctionOne exponential function shows up more often than all the others: thenatural exponential function.It is written as:Here, the base (e) is a special number calledEuler’s number(pronounced“OIL-er”, not “YOU-ler”).This number isirrational, meaning its decimal:•Never ends•Never repeatsEven though the digits maylooklike they repeat at first, they eventually don’t.Important note:You arenot expected to memorizethe value of (e), just like you don’t memorize all the digits of (π).•Answers can stay written in terms of (e), such as (12e5).•If you are asked to evaluate (ex), you are allowed to use a calculator.Preview Mode
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