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Exponential Functions o Work on Exploration 1: Exponential Functions page 22 o Definition of Exponential Function o Graphs of Exponential Growth & Decay o Applications o Rules for Exponents o Quick Review Problem 1.3

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Exploration 1: Exponential Functions Please work on the exploration on page 22 in your textbooks.

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Analyzing Exponential Functions Answer questions 1, 2, & 3

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Analyzing Exponential Functions Answer question 6

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Exponential Function If, then defines the exponential function with base a and exponent x.

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Characteristics of Exponential Functions HA y=0 a>1 function is increasing 0
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Ex 1: Find the domain and range.

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Ex 2: Find the zeros of You should be able to answer this question using Graphing – Math:Zeros Algebraically Numerically – Graphing Calc (solve, zeros)

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Ex 3: Applications – Radioactive Decay Suppose the half-life of a certain radioactive substance is 20 days and that there are 5 grams present initially. When will there be only 1 gram of the substance remaining?

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Applications – Compound Interest Compounded Interest Interest Compounded Continuously

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Determine how much time is required for an investment to double in value if interest is earned at the rate of 6.25% A) compounded monthly. B) compounded continuously. Ex 3: Applications – Compound Interest

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Review from Algebra 1 & 2 Refresh your memory on the rules of exponents on page 23. Look at the problems in the Quick Review 1.3 on page 26. Do you have any questions??

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Calculus Sections 5.1 Apply exponential functions An exponential function takes the form y = a∙b x where b is the base and b>0 and b≠1. Identify as exponential.

Calculus Sections 5.1 Apply exponential functions An exponential function takes the form y = a∙b x where b is the base and b>0 and b≠1. Identify as exponential.

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