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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.

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warm up january 30 2012
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 functions1
Exponential Functions
  • The variable is an exponent.
  • Can be written in the form
  • b is called the base. b>0, b≠1
examples
Examples

Exponential Functions

NOT Exponential

evaluating exponential functions
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
You-Try #1 (like HW #1-10)
  • Approximate using a calculator. Round to three decimal places.
graph of y b x
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
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 Natural Base, “e”
  • The irrational number “e” is called the natural base.
  • “e” is a real number similar to π
compound interest
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
Interest Compounded Yearly
  • Assume “P” dollars are invested with an annual percentage rate of “r”
compound interest formulas
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
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
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
Assignment
  • Page 364 #1-10, 19-24, 41-44, 55
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