英文微积分1.3.pptVIP

* 1.3 Exponential Functions Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2004 Yosemite National Park, CA Although some of today’s lecture is from the book, some of it is not. You must take notes to be successful in calculus. We will be using the TI-89 calculator in this class. You may use either the TI-89 Titanium or the older TI-89. TI-89 Titanium The pictures in the lectures will usually illustrate the older TI-89. Although the buttons on the Titanium Edition are different shapes and colors, they are in the same positions and have the same functions. TI-89 If $100 is invested for 4 years at 5.5% interest, compounded annually, the ending amount is: On the TI-89: ENTER At the end of each year, interest is paid on the amount in the account and added back into the account, so the amount of increase gets larger each year. This is an example of an exponential function: exponent base Graph for in a [-5,5] by [-2,5] window: MODE Graph……. FUNCTION Display Digits… FLOAT 6 Angle……. RADIAN ENTER Y= WINDOW Graph for in a [-5,5] by [-2,5] window: Y= WINDOW GRAPH Graph for in a [-5,5] by [-2,5] window: Where is ? Where is ? Where is ? Graph for in a [-5,5] by [-2,5] window: Where is ? Where is ? Where is ? What is the domain? What is the range? Population growth can often be modeled with an exponential function: Ratio: World Population: 1986 4936 million 1987 5023 1988 5111 1989 5201 1990 5329 1991 5422 The world population in any year is about 1.018 times the previous year. in 2010: About 7.6 billion people. Nineteen years past 1991. Radioactive decay can also be modeled with an exponential function: Suppose you start with 5 grams of a radioactive substance