Lab09 Exponential and Logarithmic Functions
1.) Compounding Interest - Simple Spreadsheets
Open the spreadsheet Investment Calculator and save a copy to your drive so that you may edit it. Use the spreadsheet to complete question 1. A time saving feature and one that allows exploration of "what-if" scenarios is the ability to reference cells in a formula. When you change the value of a cell that is being referenced, the formula automatically updates. For ease of use, the yellow cells are where the user should enter the varying input values and the green cells represent the desired result. a) Double click in cell B7. The formula (function) will appear in multiple colored fonts in the header bar after fx. Analyze the function. b) Use the "Simple" sheet to explore the resulting balance (A) for a principal investment of $2500 at an interest rate of 8% for 10 years. Complete the table in the lab. As you enter the new value in each of the yellow cells, what as cell B7 automatically updates. c) To compute continuous interest, the e in the formula would be entered as EXP(exponent). In cell B8, enter a function that will compute the balance when the interest is compounded continuously (notice that when you type in EXP( Sheets will show a completion and what you need to type in the parenthesis to use the EXP function).
2) Compounding Interest - Click n Drag Tables
Another time saving feature of using a spreadsheet is the ability to create a table (multiple applications of a formula) so that you can copy a formula without retyping the same formula over and over. a) Analyze the formulas in cells B7 and E7 on Sheet "Click n Drag". b) Select cell B7 on "Click n Drag" and it should be outlined with a black box on the bottom right corner. Click and drag the box on the bottom right corner of the cell and drag it so that B7 to B12 (B7:B12) are covered. When you release the clicker, the boxes should be filled with the formula and the balance should appear. c) Instead of clicking and dragging, you can also copy and paste. Select cell E7. Press Ctrl + c to copy. Select cell E8:E12 and press Ctrl + v to paste the formula. Again, analyze the formulas in cells E8:E12.
3) Exponential Functions
In the following applet, explore the affects of changing a, b, h and k.
Exploring Exponential Functions
4) Exploring Logarithmic Functions
5) The mathematical Constant e
* Read about e onWikipedia. * One place where e comes up is when we calculate continuously compounded interest. If we take the part out of the compound interest formula, continuously compounded interest occurs when (n approaches infinity) or the frequency at which interest is compounded at all times. Graph on your calculator. Determine the equation of the horizontal asymptote by looking an infinitely higher x values in the table OR using the Trace feature on the graph. BONUS: Make a "Click n Drag" table in a spreadsheet and paste the table in you lab. The table should show n =1, 2, 5, 10, 50, 100, 10000, 1000000000000 and the resulting value form your equation.