Chapter 9 Exponential Functions Class Notes Geometric Sequences

Chapter 9 – Exponential Functions Class Notes

Geometric Sequences Lesson 9. 1

Extending Geometric Sequences – In a geometric sequence, the ratio of successive terms is the same number r, called the common ratio. – Geometric sequences can be though of as functions. The term number, or position in the sequence, is the input, and the term itself is the output

Extending Geometric Sequences

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Finding the nth Term of a Geometric Sequence

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Exponential Functions Lesson 9. 2

Evaluating an Exponential Function – The types of functions in which the independent variable appears in an exponent is an exponential function.

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Identifying an Exponential Function – Remember that linear functions have constant first differences and quadratic functions have constant second differences. – Exponential functions do not have constant differences but they do have constant ratios.

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– To graph an exponential function, choose several values of x (positive, negative and 0) and generate ordered pairs. – Plot the points and connect them with a smooth curve

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Graphs of Exponential Functions

Exponential Growth and Decay Lesson 9. 3

Exponential Growth – Exponential growth occurs when a quantity increases by the same rate r in each time period t.

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Compound Interest – Compound interest is interest earned or paid on both the principal and previously earned interest.

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Exponential Decay – Exponential decay occurs when a quantity decreases by the same rate r in each time period t.

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Half Life

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Linear, Quadratic, and Exponential Models Lesson 9. 4

Graphing Data to Choose a Model

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Using Patterns to Choose a Model

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General Forms of Functions

Comparing Functions Lesson 9. 5

Comparing Linear Functions

Comparing Exponential Functions –

Comparing Quadratic Functions –