This document discusses exponential functions and exponential growth. It explains that an exponential function involves the expression bx, where b is the base. It provides instructions for graphing exponential functions by plugging in x and plotting points. Exponential growth can be modeled by the equation where a is the initial amount, r is the interest rate, and t is the time.

1. Exponential GrowthAlgebra 28.1p. 465

2. What is a function?

3. What types of functions have we learned so far?Review

4. An exponential function involves the expression bx.

5. An exponential function involves the expression bx.The base (b) is a positive number other than 1.

6. Graphing Exponential Functions

7. Plug in x.Plot each point (x, f(x)).Graphing Exponential Functions

8. Plug in x.Plot each point (x, f(x)).Graphing Exponential Functions

9. Plug in x.Plot each point (x, f(x)).Graphing Exponential Functions

10. Graphing Exponential Functions

11. Graphing Calculator Comparisons

12. Graph y = a2x, which has a y-intercept at (0, a).y = abx-h + k

13. Graph y = a2x, which has a y-intercept at (0, a).Shift the graph vertically kspaces.y = abx-h + k

14. Graph y = a2x, which has a y-intercept at (0, a).Shift the graph vertically kspaces.Shift the graph horizontally hspaces.Note that you are moving opposite the sign in front of h.y = abx-h + k

15. When something increases by a fixed percent each year (or time period), it can be modeled by the equation:Exponential Growth

16. a is the initial amountExponential Growth

17. a is the initial amount

18. r is the interest rateExponential Growth

19. a is the initial amount

20. r is the interest rate

21. t is the timeExponential Growth