7-2 PROPERTIES OF EXPONENTIAL
FUNCTIONS
GRAPH EXPONENTIAL FUNCTIONS BY EXPLORING THE PROPERTIES OF
FUNCTIONS OF THE FORM 𝑦 = 𝑎𝑏 𝑥 .
TRANSFORMING EXPONENTIAL FUNCTIONS
• THE PARENT FUNCTION IS 𝑦 = 𝑏 𝑥
• GENERAL FORM OF AN EXPONENTIAL FUNCTION: 𝑦 = 𝑎𝑏 (𝑥−ℎ) + 𝑘
• 𝑎 REPRESENTS A STRETCH OR COMPRESSION
• EX: 𝑦 = 3 ∙ 2𝑥
• ℎ REPRESENTS THE HORIZONTAL TRANSLATION
• EX: 𝑦 = 2(𝑥−4)
• 𝑘 REPRESENTS THE VERTICAL TRANSLATION
IRRATIONAL BASES
• SO FAR, WE HAVE WORKED WITH RATIONAL BASES, BUT THE BASE OF AN EXPONENTIAL
FUNCTION CAN BE IRRATIONAL AS WELL.
• MOST COMMON IRRATIONAL BASE IS 𝑒.
• THESE ARE CALLED NATURAL BASE EXPONENTIAL FUNCTIONS
• DESCRIBE CONTINUOUS GROWTH OR DECAY
• SAME PROPERTIES AS OTHER EXPONENTIAL FUNCTIONS
• 𝑒 ≈ 2.71828
• EVALUATING CAN BE DONE BY USING A CALCULATOR
• EX: 𝑒 3
• USE 𝑒 𝑥 KEY ON CALCULATOR
• GRAPH 𝑦 = 𝑒 𝑥 AND EVALUATE FOR X = 3
• USE A TABLE OF VALUES FOR 𝑦 = 𝑒 𝑥
CONTINUOUSLY COMPOUNDED INTEREST
• SUPPOSE YOU WON A CONTEST AT THE START OF 5TH GRADE THAT DEPOSITED $3000 IN AN
ACCOUNT THAT PAYS 5% ANNUAL INTEREST COMPOUNDED CONTINUOUSLY. HOW MUCH
WILL BE IN THE ACCOUNT WHEN YOU ENTER HIGH SCHOOL? ROUND TO THE NEAREST
DOLLAR.
• 𝐴 4 = 3000 ∙ 𝑒 0.05
• A(4) = $3664
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ASSIGNMENT
• ODDS P.447 #17-35