Unit+8

=Unit 8 Exponential and Logarithmic Functions=

Vocabulary

 * asymptote (p. 425) || decay factor (p. 425) || logarithmic equation (p. 455) ||
 * Change of Base Formula (p. 453) || exponential equation (p. 453) || logarithmic function (p. 440) ||
 * common logarithm (p. 439) || exponential function (p. 422) || natural logarithmic function (p. 462) ||
 * continuously compounded interest formula (p. 433) || growth factor (p. 422) ||  ||
 * || logarithm (p. 439) ||

8-1 Objectives
The general form of an **exponential function** is //y// = //ab////x//, where //x// is a real number, //a// â‰ 0 , //b// > 0 , and //b// â‰ 1. When //b// > 1, the function models exponential growth, and //b// is the **growth factor**. When 0 < //b// < 1, the function models exponential decay, and //b// is the **decay factor**.
 * 1) To model exponential growth (p. 422)
 * 2) To model exponential decay (p. 424)

8-2 Objectives
Exponential functions can be translated and reflected. The graph of //y// = //ab////x// 8 âˆ’ //h// + //k// is the graph of //y// = //ab////x// translated //h// units horizontally and //k// units vertically. The **continuously compounded interest** formula is //A// = //Pe////rt//, where //P// is the principal, //r// is the annual rate, and //t// is time in years.
 * 1) To identify the role of constants in //y// = //ab////cx// (p. 431)
 * 2) To use //e// as a base (p. 433)

8-3 Objectives
If //y// = //b////x//, then log//b// //y// = //x//. The **logarithmic function** is the inverse of the exponential function, so the graphs of the functions are reflections of one another over the line //y// = //x//. Logarithmic functions can be translated and reflected. When //b// = 10, the logarithm is called a **common logarithm**, which you can write as log //y//.
 * 1) To write and evaluate logarithmic expressions (p. 438)
 * 2) To graph logarithmic functions (p. 440)

8-4 Objectives
For any positive numbers, //M//, //N//, and //b//, //b// â‰ 1, each of the following statements is true. Each can be used to rewrite a logarithmic expression.
 * 1) To use the properties of logarithms (p. 446)
 * log//b// //MN// = log//b// //M// + log//b// //N//, by the Product Property
 * log//b// [[image:http://www.pearsonsuccessnet.com/snpapp/iText/products/0-13-037881-X/Ch08/08EM/images/Ch08_SecCR_im003.gif width="13" height="28"]] = log//b// //M// âˆ’ log//b// //N//, by the Quotient Property
 * log//b// //M////x// = //x// log//b// //M//, by the Power Property

8-5 Objectives
An equation in the form //b////cx// = //a//, where the exponent includes a variable, is called an **exponential equation**. You can solve exponential equations by taking the logarithm of each side of the equation. An equation that includes a logarithmic expression is called a **logarithmic equation**.
 * 1) To solve exponential equations (p. 453)
 * 2) To solve logarithmic equations (p. 455)

8-6 Objectives
The inverse of //y// = //e////x// is the **natural logarithmic function** //y// = log//e// //x// = ln //x//. You solve natural logarithm equations in the same way as common logarithm equations.
 * 1) To evaluate natural logarithmic expressions (p. 462)
 * 2) To solve equations using natural logarithms (p. 463)

Unit 8 Review