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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

• 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