Chapter 4 (F11)

Chapter 4 (F11) - Section 4.1 Exponential Functions...

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Section 4.1 – Exponential Functions Exponential Functions are of the form : ( ) ( 0, 1) x f x b b b = Example : Graph ( ) 2 x f x = x y = 2 x –3 –2 –1 0 1 2 3 Domain: x -intercept: Vertical Asymptote: Range: y -intercept: Horizontal Asymptote: Example : Graph ( 29 1 4 ( ) x f x = x y = (¼) x –3 –2 –1 0 1 2 3 Domain: x -intercept: Vertical Asymptote: Range: y -intercept: Horizontal Asymptote: 1
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Note: ( ) x f x b = is an increasing function when b > 1 and ( ) x f x b = is a decreasing function when 0 < b < 1 The number e (the natural base): ( 29 1 1 n n e as n = + → ∞ 2.71828. .. e Example : Graph ( ) x f x e = on your calculator. Examples : Graph the transformations and list the new domain and range. a) ( ) 2 3 x f x = + b) 2 ( ) 2 x f x + = c) ( ) 2 x f x e - = - d) ( ) x f x e = - 2
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Compound Interest Formulas: Compound Interest : A = ( 29 nt n r P + 1 Continuous Compounding : A = rt Pe I = interest P = principal A = amount after t years t = time in years r = per annum interest rate (decimal) n = # of compounding periods per year Examples : 1. Suppose $1,500 is placed in a savings account that earns 2.3% per year. How much money will be in the account after 10 years if the interest is compounded: a) Annually? b) Semi-annually? c) Quarterly? d) Monthly? e) Daily? f) Continuously? 3
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Section 4.2 – Logarithmic Functions Logarithmic Functions are of the form : ( ) log ( 0, 1, 0) b f x x b b x = ( b = base, x = argument) log y b y x b x = = Example : Change the following from logarithmic form to exponential form: a) 6 log 2 x = b) 3 log x m = Example : Change the following from exponential form to logarithmic form: a) 5 10 x = b) P M Q = Example : Find the exact value of: a) 3 log 27 b) ( 29 1 2 8 log 4
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Special Logarithms : The “common logarithm” 10 log x = The “natural logarithm”
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This note was uploaded on 01/06/2012 for the course MATH 1314 taught by Professor Lisajuliano during the Spring '12 term at Collins.

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Chapter 4 (F11) - Section 4.1 Exponential Functions...

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