Today in Precalculus Notes: Intro to Exponential Functions (no handout) Homework.

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Presentation transcript:

Today in Precalculus Notes: Intro to Exponential Functions (no handout) Homework

Exponential Functions Functions where the exponent is the variable. y=ab x, where a is non-zero and represents the initial value f(0) b is positive and represents the base If b>1 exponential growth If 0<b<1 exponential decay

Exponential Functions Example: The initial quantity is 10, and base is ½

Exponential Functions Which of the following are exponential functions? If they are, list the initial value and the base 1. y = 9 x 2. y = 37 x 3. y = x y = 20.4 x Yes, initial value is 1 and base is 9 Yes, intial value is 3 and base is 7 No, exponent is not a variable Yes, initial value is 2 and base is 0.4

Exponential Functions To calculate the value of the functions, be sure to follow the order of operations. Example: y = 37 x x = 2 y = 37 2 y = 349 y = 147

Graphs y = 2 x

Graphical Transformations y = 2 x+2

Graphical Transformations y = -2 x

Exponential Functions Determine the formula for the exponential function whose values are given in the following table y = 34 x xy -23/16 3/

Exponential Functions Determine the formula for the exponential function whose values are given in the following table xy /3

Homework Page 286: 1-12all, 25-30all but just part a