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Warm-Up: January 30, 2012

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- 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

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

Exponential Functions

NOT Exponential

- 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

- Approximate using a calculator. Round to three decimal places.

- 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

- 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 irrational number “e” is called the natural base.
- “e” is a real number similar to π

- 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)

- Assume “P” dollars are invested with an annual percentage rate of “r”

- If interest is compounded “n” times a year for “t” years
- If interest is compounded continuously for “t” years

- 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?

- 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?

- Page 364 #1-10, 19-24, 41-44, 55