Week 6- Exponential and Logarithmic Functions (13.1-13.3).docx

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Exponential and Logarithmic Functions (Sections 13.1-13.3) 13.1 Exponential Function Definitions: The exponential function is defined as y = b x where b > 0, b≠ 1 (i.e. b is a positive constant), and x is any real number (i.e. x is the variable) In the function defined above, b is called the base , and x is the exponent Exercise 1: Given the exponential functions y = 2 x , y = ( 1 2 ) a) fill out the table of values below b) graph the functions c) state the domain and range of the function (i.e. what values of x are allowed and what values of y are obtained) d) what happens to the value of y as x increases? e) what is special about the x ¿ axis x y = 2 x y = ( 1 2 ) x -3 -2 -1 0 1 2 3 x Page 1 of 13
Conclusions (Basic Properties of the Exponential Function): The domain is all values of x ; the range is y > 0 The x ¿ axis is an asymptote of the of y = b x . As x increases, o b x increases if b > 1 o b x decreases if b < 1 The standard, basic shape of an exponential function takes the form: Applications of Exponential Functions: Exponential functions are used in electronics, mechanical systems, thermodynamics, nuclear physics, biology – in Page 2 of 13 b > 1 0 < b < 1
studying population growth, and in business – in calculating compound interest.

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