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Exponential Functions and Graphs

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Section 4.2 Exponential Functions and Graphs Exponential Function The exponential function is very important in math because it is used to model many real life ... – PowerPoint PPT presentation

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Title: Exponential Functions and Graphs


1
Section 4.2
  • Exponential Functions and Graphs

2
Exponential Function
  • The exponential function is very important in
    math because it is used to model many real life
    situations.
  • For example population growth and decay,
    compound interest, economics, and much more.

3
Exponent
  • Remember

4
Exponential Function
  • The function f(x) ax, where x is a real number,
    a gt 0 and a ? 1, is called the exponential
    function, base a.
  • The base needs to be positive in order to avoid
    the complex numbers that would occur by taking
    even roots of negative numbers.
  • Examples

5
Graphing Exponential Functions
  • To graph an exponential function, follow the
    steps listed
  • 1. Compute some function values and list
  • the results in a table.
  • 2. Plot the points and connect them with a
  • smooth curve. Be sure to plot enough
  • points to determine how steeply the
  • curve rises.

6
Example
  • Graph the exponential function y f(x) 3x.

7
Example
  • Graph y 3x 2.
  • The graph is the graph of y 3x shifted _____ 2
    units.

8
Example
  • Graph the exponential function

9
Example
  • Graph y 4 ? 3?x
  • The graph is a reflection of the graph of y 3x
    across the _______, followed by a reflection
    across the _______ and then a shift _______ of 4
    units.

10
Observing Relationships
11
Connecting the Concepts
12
The Number e
  • e is known as the natural base
  • (Most important base for exponential
  • functions.)
  • e is an irrational number
  • (cant write its exact value)
  • We approximate e

13
The Number e
  • Find each value of ex, to four decimal places,
    using the ex key on a calculator.
  • a) e4
  • b) e?0.25
  • c) e2
  • d) e?1

14
Natural Exponential Function
  • Remember
  • e is a number
  • e lies between 2 and 3

15
Graphs of Exponential Functions, Base e
  • Graph f(x) ex.

16
Example
  • Graph f(x) ex2.

17
Example
  • Graph f(x) 2 ? e?3x.

18
Compound Interest Formula
19
Example
  • A father sets up a savings account for his
    daughter. He puts 1000 in an account that is
    compounded quarterly at an annual interest rate
    of 8.
  • How much money will be in the account at the end
    of 10 years? (Assume no other deposits were made
    after the original one.)
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