Warm up january 30 2012
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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

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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 functions

Exponential Functions

Section 3.1


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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