Exponential Functions Chapter 10, Sections 1 and 6

What are exponential functions? Exponential functions are functions that have a variable as an exponent ▫“a” and “b” are real numbers ▫a≠0, b>0, b≠1

Properties of Exponential Functions Continuous One-to-one function The domain is all real numbers The range is positive if a>0 The range is negative if a<0 The x-axis is an asymptote The y-intercept is (0,a)

Exponential Equations and Inequalities When the bases are the same, the exponents can be set equal to each other. When the bases are not the same, graph and find the intersection(s)

Examples – Solve the following

More about Exponential Functions To simplify expressions with exponents, follow the rules of exponents To write an exponential function that passes through two points, use an exponential regression If b>1, the function is an exponential growth If 0<b<1, the function is an exponential decay

Exponential Decay Examples include depreciation of value and radioactive decay

Exponential Growth Examples include population increase, bacteria growth

Compound Interest

Half-Life

Important… If the problem gives you a formula to use, then use that formula. If the problem does NOT give you a formula to use, then use either the growth formula or the decay formula.

Classwork/Homework – growth and decay handout Exit slip – What is a real-life example of exponential growth and exponential decay?