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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.)