Warm-Up: January 30, 2012

1 / 16

# Warm-Up: January 30, 2012 - PowerPoint PPT Presentation

Warm-Up: January 30, 2012. In what directions and how far would you have to move the graph of f(x) to get the graph of f(x+3)+5?. Exponential Functions. Section 3.1. Exponential Functions. The variable is an exponent. Can be written in the form b is called the base . b&gt;0, b≠1.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Warm-Up: January 30, 2012' - sook

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Warm-Up: January 30, 2012
• In what directions and how far would you have to move the graph of f(x) to get the graph of f(x+3)+5?

### Exponential Functions

Section 3.1

Exponential Functions
• The variable is an exponent.
• Can be written in the form
• b is called the base. b>0, b≠1
Examples

Exponential Functions

NOT Exponential

Evaluating Exponential Functions
• Use the “^” on the TI-83 for exponents
• Put ()’s around fractions or other expressions that are either the base or exponent
• DO NOT put ()’s around a·b
You-Try #1 (like HW #1-10)
• Approximate using a calculator. Round to three decimal places.
Graph of y=bx
• Domain is all real numbers, (-∞, ∞)
• Range is all positive numbers, (0, ∞)
• The y-intercept is 1
• The graph is monotonically increasing for b>1
• The graph is monotonically decreasing for 0<b<1
• The x-axis is a horizontal asymptote
• The graph is one-to-one
Transformations of
• Similar to transformations we’ve seen before
• “d” shifts the graph right/left
• “c” shifts the graph up/down
• “a” stretches/shrinks the graph
• Negatives in a or x cause reflections
The Natural Base, “e”
• The irrational number “e” is called the natural base.
• “e” is a real number similar to π
Compound Interest
• Suppose you want to invest money. The amount that you invest is called the principal, designated by “P”.
• Compound interest is when you receive interest on previous interest in addition to on your principal.
• The investment’s interest depends on the annual percentage rate, r, which is expressed as a decimal (i.e., 5%  0.05)
Interest Compounded Yearly
• Assume “P” dollars are invested with an annual percentage rate of “r”
Compound Interest Formulas
• If interest is compounded “n” times a year for “t” years
• If interest is compounded continuously for “t” years
Example 6 (like HW #41-44)
• Suppose that you have \$5000 to invest. Which investment yields the greatest return over 5 years: 5.25% compounded quarterly or 5.1% compounded continuously?
You-Try #6 (like HW #41-44)
• Suppose that you have \$2000 to invest. Which investment yields the greatest return over 2 years: 4.5% compounded monthly or 4.3% compounded continuously?
Assignment
• Page 364 #1-10, 19-24, 41-44, 55