exponentialfunctions-140119191324-phpapp01.pptx

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1. Exponential Functions

2. The exponential function is very important in math because it is used to model many real life situations. For example: population growth and decay, compound interest, economics, and much more. Why is it important?

3. Question… Definition of Exponential Function How is this function different from functions that we have worked with previously?

4. The exponent is the variable! Answer: b = The base b >0 and b ≠ 1 x = The exponent x=any real number Question… Is f(x)=x 3 an exponential function? NO

5. One of the most common exponential functions is The graph looks like this: The Graph of an exponential function

6. The graph starts off slow but then increases very rapidly The x-axis (y=0) is an asymptote. X can be any real number, for example: (0,1) is the y intercept Models Exponential Growth

7. What would a graph look like if b is between 0 and 1? For example : Question …

8. The graph starts off very high but then decreases very rapidly The x-axis (y=0) is an asymptote. X can be any real number, for example: (0,1) is the y intercept Models Exponential Decay

9. Recap b = The base b >0 and b ≠ 1 x = The exponent x=any real number Definition b>1 0<b<1

10. Exponential Solving Equations

11. Question… What is an exponential equation? An equation where the variable is the exponent. Example:

12. How do we solve this? Any ideas? What if we changed the right side to Now What?

13. Set the exponents equal! If Then x =? Check : 2 -3 = Then we have solved

14. Express each side of the equation as a power of the same base. Set the exponents equal and solve. Check your answer Solving Exponential Equations If the bases are the same, set the exponents equal! Main idea

15. Let’s look at some examples! Solve for x: Are the bases equal? YES Set the exponents equal. Solve for x. All we have here is a simple Algebra problem

16. Check your answer: x = -1 It checks!

17. Solve for x: Example # 2 Are the bases equal? NO Change the right side to: Simplify: Solve!

18. Check your answer: t = 2 It checks!

19. Solve for x: Last Example

20. Solve for x: Solution Are the bases equal? NO Change both sides to: Simplify: Solve!

21. Check your answer: x = 11/4 It checks!

22. REVIEW 1 . Exponential function: The exponent is the variable Key Point: b = the base b >0 and b ≠1 X = the exponent X = any real number 2 . Exponential Equations: An equation where the exponent is the variable Example: How to solve: If the bases are the same, set the exponents equal! Rewrite as : Set exponents equal : Solve : Check: It checks!

23. Any Questions??? Homework: Exponential Equations Worksheet