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## Exponential Functions

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**Exponential Functions**Section 3.1**Objectives**• Evaluate an exponential function at a given point. • Determine the equation of an exponential function given a point or two points. • Graph an exponential function. • State the domain and range of an exponential function. • Determine the transformation of a transformed exponential function given an equation. • Solve a word problem involving an exponential function.**Vocabulary**• exponential function • base of an exponential function • natural exponential function**Formula**• basic exponential function where a > 0 and a≠ 1**Graph the function**What it the domain of the function? What is the range of the function? What is(are) the x-intercepts? What is(are) the y-intercepts?**Find the exponential function**whose graph goes through the points (0, 5) and (3, 40).**Suppose you go to a company that pays $0.04 for the first**day, $0.08 for the second day, $0.16 for the third day, and so on. If the daily wage keeps doubling, what will your income be on the 30th day?**Finance Formula**• discrete compound interest • continuous compound interest