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# 8 6 Graphing Exponential Expressions

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### 8 6 Graphing Exponential Expressions

1. 1. Back to Graphing Chapter 8.6 Exponential Functions Principal Formula
2. 2. General Growth Formula <ul><li>A = P (1 + r) t </li></ul><ul><li>P = the original amount </li></ul><ul><ul><li>sometimes called the principal </li></ul></ul><ul><li>r = rate of change </li></ul><ul><li>t = time </li></ul>
3. 3. Using General Growth Formula <ul><li>A = P (1 + r) t </li></ul><ul><li>Deposit \$475 into and interest-bearing account at 3.75%. How much will be in the account after two years? </li></ul><ul><li>P is the deposit (principal). </li></ul><ul><li>Rate is .0375 (converted from percentage) </li></ul><ul><li>Time is 2 years. </li></ul><ul><li>A = 475(1+.0375) 2 </li></ul>
4. 4. A = Find the Amount in the bank <ul><li>A = 475(1.0375) 2 </li></ul><ul><li>A = 475(1.07640625) </li></ul><ul><li>A = 511.2929688 </li></ul><ul><li>In money, \$511.29 </li></ul>
5. 5. A = P (1 + r) t <ul><li>According to 1991 records, 866 million people lived in the SE Asian country, India. At the time, it was growing at a rate of 1.9%. At this rate, what would be the population in 1996? </li></ul><ul><li>P is the present population. </li></ul><ul><li>Rate is .019 (converted from percentage) </li></ul><ul><li>Time is 5 years. </li></ul><ul><li>A = 866(1+.019) 5 </li></ul>
6. 6. A = 866 million(1+.019) 5 <ul><li>A = 866(1.019) 5 </li></ul><ul><li>A = 866(1.098679244) </li></ul><ul><li>A = 951.4562254 million </li></ul><ul><li>Approximately 951, 456, 000 </li></ul>
7. 7. Graphing Exponential Functions
8. 8. How to Graph y =2 x <ul><li>We can start with an x/y box. </li></ul><ul><li>This is sort of a mathematical experiment. </li></ul><ul><li>Follow these steps: </li></ul><ul><li>We can then fill in some values for x. </li></ul><ul><li>Insert the x-values into the equation to find y. </li></ul><ul><li>Graph the (x,y) values </li></ul>
9. 9. y =2 x <ul><li>y = 2 -2 </li></ul><ul><li>y = 2 -1 </li></ul><ul><li>y = 2 0 = 1 </li></ul><ul><li>y = 2 2 = 4 </li></ul><ul><li>y = 2 3 = 8 </li></ul><ul><li>X Y </li></ul><ul><li>-2 </li></ul><ul><li>-1 </li></ul><ul><li>0 </li></ul><ul><li>+1 </li></ul><ul><li>+2 </li></ul><ul><li>+3 </li></ul>
10. 10. y =2 x <ul><li>y = 2 -2 </li></ul><ul><li>y = 2 -1 </li></ul><ul><li>y = 2 0 = 1 </li></ul><ul><li>y = 2 2 = 4 </li></ul><ul><li>y = 2 3 = 8 </li></ul><ul><li>X Y </li></ul><ul><li>-2 </li></ul><ul><li>-1 </li></ul><ul><li>0 1 </li></ul><ul><li>+1 2 </li></ul><ul><li>+2 4 </li></ul><ul><li>+3 8 </li></ul>
11. 11. Graph the results <ul><li>(2, ¼) </li></ul><ul><li>(1, ½) </li></ul><ul><li>(0,1) </li></ul><ul><li>(1,2) </li></ul><ul><li>(2,4) </li></ul><ul><li>(3,8) </li></ul>
12. 12. <ul><li>y =2 x </li></ul>Is it possible to get a negative y value?
13. 13. ONLINE Graphing Calculator <ul><li>Can be found at this URL: </li></ul><ul><li>http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html </li></ul><ul><li>OR CLICK HERE during the presentation. </li></ul>
14. 14. Extra