1. Section 8-2 Properties of Exponential Functions

2. Asymptote Is a line that a graph approaches as x or y increases in absolute value.

3. Example Graph y = 3 2 x and y = –3 2 x. Label the asymptote of each graph.

4. Example Graph y = 3 2 x and y = –3 2 x. Label the asymptote of each graph.

5. Example 2 – Look at the graph and identify the asymptotes

6. Half - life Of a radio active substance is the time it takes for half of the material to decay or decompose. The decay factor is.5

7. Example Suppose a hospital prepares a 100-mg supply of technetium – 99m, which has a half life of 6 hours. Make a table showing the amount of technetium –99m remaining at the end of each 6- hour interval for 36 hours? Write the equation to describe the exponential function? Use the function to find the amount after 75 hours? # of 6hr half lives Technetium- 99m Present (mg)

8. Example Suppose a hospital prepares a 100-mg supply of technetium – 99m, which has a half life of 6 hours. Make a table showing the amount of technetium –99m remaining at the end of each 6- hour interval for 36 hours? Write the equation to describe the exponential function? Use the function to find the amount after 75 hours? # of 6hr half lives Technetium- 99m Present (mg)

9. Example Suppose a hospital prepares a 100-mg supply of technetium – 99m, which has a half life of 6 hours. Make a table showing the amount of technetium –99m remaining at the end of each 6- hour interval for 36 hours? Write the equation to describe the exponential function? Use the function to find the amount after 75 hours? # of 6hr half lives Technetium- 99m Present (mg)

10. Example Suppose a hospital prepares a 100-mg supply of technetium – 99m, which has a half life of 6 hours. Make a table showing the amount of technetium –99m remaining at the end of each 6- hour interval for 36 hours? Write the equation to describe the exponential function? Use the function to find the amount after 75 hours? # of 6hr half lives Technetium- 99m Present (mg)

11. Example Suppose a hospital prepares a 100-mg supply of technetium – 99m, which has a half life of 6 hours. Make a table showing the amount of technetium –99m remaining at the end of each 6- hour interval for 36 hours? Write the equation to describe the exponential function? Use the function to find the amount after 75 hours? # of 6hr half lives Technetium- 99m Present (mg)

12. The number e When interest is compounded continuously the formula can be simplified using the number e. The formula for continuously compounded interest is: A = P e rt

13. The number e When interest is compounded continuously the formula can be simplified using the number e. The formula for continuously compounded interest is: A = P e rt

14. Example You invest $1050 at an annual interest rate of 5.5% compounded continuously. How much will you have after 5 years?

15. Example You invest $1050 at an annual interest rate of 5.5% compounded continuously. How much will you have after 5 years?

16. Example You invest $1050 at an annual interest rate of 5.5% compounded continuously. How much will you have after 5 years?

17. Checking For Understanding Do not email 1. Use the formula A = Pe rt to find the amount in a continuously compounded account where the principal is $2000 at an annual interest rate of 5% for 3 years. 2. Evaluate e to four decimal places. 1313