Algebra 2 9 1 Exponential Functions ly abx

Algebra 2 9. 1 Exponential Functions ly = abx la = 0, b > 0 & b = 1

Characteristics of an Exponential Function l l l Function is continuous and one-to-one Domain is the set of all real numbers x-axis is an asymptote of the graph Range is the set of all positive numbers if a > 0 and all negative numbers if a < 0 The graph contains the point (0, a). . . y-intercept is a.

Exponential Growth & Decay l l GROWTH: y = abx : a > 0 , b > 1 Example of Exponential Growth: y = 4(2)x DECAY: y = abx : a > 0 , 0 < b < 1 Example of Exponential Decay: y = 7(½)x

Determine whether each function represents exponential growth or decay. l l l Ex. 1 y=(1/5)x – Decay l Ex. 4 y = (0. 7)x – Decay Ex. 2 y = 3(4)x – Growth l Ex. 5 y = ½(3)x – Growth l Ex. 6 y = 10(4/3)x – Growth Ex. 3 y = 7(1. 2)x – Growth

Properties of Exponents

Simplify these expressions using the properties of exponents Ex 7 Ex 8 Ex 9

Exponential Equations in which variables occur as exponents. b = 1, bx = by then x = y l Example: 2 x = 28, then x = 8 l Only works when both sides have the same bases

Solving exponential equations Example 10 Rewrite 81 with a base of 3 Since the bases are equal, set the exponents equal and solve Solve for n

Solving exponential equations Example 11 Rewrite both sides with the same base of 2 Simplify by multiplying the powers Set the exponents equal Solve for x

l Ex 12 Solve the following two equations. Ex 13

Exponential Inequalities l l If b > 1, then bx > by if and only if x > y, and bx < by if and only if x < y For example: 5 x < 54, then x < 4

Homework Assignment #56 l p. 504 20, 23 -26, 31, 33, 42 -46, 65, 66