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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. 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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  1. 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?

  2. Exponential Functions Section 3.1

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

  4. Examples Exponential Functions NOT Exponential

  5. 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

  6. You-Try #1 (like HW #1-10) • Approximate using a calculator. Round to three decimal places.

  7. 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

  8. 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

  9. The Natural Base, “e” • The irrational number “e” is called the natural base. • “e” is a real number similar to π

  10. 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)

  11. Interest Compounded Yearly • Assume “P” dollars are invested with an annual percentage rate of “r”

  12. Compound Interest Formulas • If interest is compounded “n” times a year for “t” years • If interest is compounded continuously for “t” years

  13. 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?

  14. 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?

  15. Assignment • Page 364 #1-10, 19-24, 41-44, 55

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