1. Exponential Functions Acadia National Park, Maine

2. I will be using the TI-nspire cx CAS calculator in this class. I will do my best to support whatever model calculator you have. After turning the calculator on, push the Scratchpad key to get ready to work.

3. If $100 is invested for 4 years at 5.5% interest, compounded annually, the ending amount is: On the TI-nspire: 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 enter

4. Graph for in a [-5,5] by [-2,5] window: Start by pressing the scratchpad key again to switch to graphing mode. Press menu Scroll down to3: Graph Entry/Edit 1: Functionshould be highlighted. enter Press Input in the entry line. enter Press or just press 3 enter and press

5. Graph for in a [-5,5] by [-2,5] window: To enter the next two functions, we are going to repeat some of the previous steps, but we will use a shortcut to save keystrokes.

6. Graph for in a [-5,5] by [-2,5] window: Press menu 1: Function should be highlighted. enter Press Input in the entry line. enter Press Input in the entry line. Instead of pressing enter, press the down arrow once to get out of the exponent box and a second time to get a new entry line. Press 3

7. Graph for in a [-5,5] by [-2,5] window: Next we will change the dimensions of the viewing window.

8. Press when finished. enter Graph for in a [-5,5] by [-2,5] window: Press menu Scroll down to 4: Window / Zoom or just press 4 enter and press 1: Window Settings… is highlighted. Input the appropriate values on each line, using the key to move between lines. tab enter Press This is a negative sign, which on the calculator is different from a minus sign. Use.

9. Graph for in a [-5,5] by [-2,5] window: Where is ?

10. Graph for in a [-5,5] by [-2,5] window: Where is ? What is the domain?What is the range?

11. 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.

12. Radioactive decay can also be modeled with an exponential function: Suppose you start with 5 grams of a radioactive substance that has a half-life of 20 days. When will there be only one gram left? After 20 days: 40 days: t days: In Pre-Calc you solved this using logs. Today we are going to solve it graphically for practice.

13. Press menu Before we start, we need to clear the previous graph. Next we will input the new functions and new viewing window. If you want to clear the entire scratchpad, including the axis: Press doc_ 1 Actions 4 Delete All enter Yes B Clear Scratchpad To get back to the graph screen, press

14. Press menuenter Press enter Press Press the down arrow. Press 3 Input in the entry line for. Press: menu Press when finished. enter Input the appropriate values using the key to move between lines. tab Use the right arrow to get out of the parentheses. 4 Window / Zoom 1 Window Settings Hint: If you have already entered one equation and are viewing the graph, a shortcut for entering another equation is to use the key. tab

15. We will use the calculator to find a decimal approximation for the intersection. Press menu Notice that both graphs are flashing, if there had been more than two graphs, you would choose which ones you want to use. Use the touchpad to move the lower bound to the left of the intersection, and push Enter. Use the touchpad to move the upper bound to the right of the intersection, and push Enter. 6 Analyze Graph 4 Intersection

16. The calculator has found the intersection, although it is a little difficult to read. There will be one gram of the substance left in approximately 46 days. You can hover over the number and push the + button to increase the significant digits, then push Enter.

17. We can also clean up the graph by moving the labels. Press to put the label in its new position. esc While hovering over a label, push and to “grab” the label. Then drag it to a new position. ctrl

18. We can change the color of a graph: While hovering over a graph, press ctrl menuenter 9 Color Use the arrows to select a color, then either click or press. Then press again. enter

19. Many real-life phenomena can be modeled by an exponential function with base, where. e can be approximated by: Graph: y=(1+1/x)^x in a [0,10] by [-5,10] window. Use “trace” to investigate the function. menuenter Use the touchpad to move left and right along the curve. 5 Trace

20. Tab to Table Step, change it to 1000, and press Enter. menuenter We can have the calculator construct a table to investigate how this function behaves as x gets much larger. Press menu To change the table settings, press Use the down arrow on the touch pad to scroll down to watch the y value approach e. 7 Table 2 5 Edit Table Settings

21. menu To remove the table, press: 2 Table 1 Remove Table 