Warm up

1. Warm up Simplify the following: 1.) 2.) 3.) 4.)

2. Chapter 8.7 Exponential Functions What is an exponential function? - it is a function in the form y = a **Today’s objectives** - Evaluating an exponential function with a given domain. - Graphing exponential functions. - Applying exponential functions to real-world problems

3. Evaluating an exponential funciton y = for when x = 2, 3, 4

4. Evaluating an exponential funciton y = for the domain {-3, 6}

5. Evaluating an exponential funciton Try one on your own… y = for when x = -2, -1, 0

6. Exponential functions and their graphs

7. How do we graph an exponential function? Step 1: set a domain (typically -2, -1, 0, 1, 2). Step 2: make a table of values. Step 3: graph. Graph y =

8. How do we graph an exponential function? Step 1: set a domain (typically -2, -1, 0, 1, 2). Step 2: make a table of values. Step 3: graph. Graph y =

9. How do we graph an exponential function? Step 1: set a domain (typically -2, -1, 0, 1, 2). Step 2: make a table of values. Step 3: graph. Graph y =

10. Real-world examples of exponential functions Suppose rabbits are taken to an island. The rabbit population then triples every half year. Write an exponential function where x is the number of half-year periods. How many rabbits would there be after 2 years? 1620 rabbits

11. Suppose 10 animals are taken to an island, and then the population of these animals quadruples every year. Write an exponentials equation to represent this growth. How many animals would there be after 6 years? 40,960

12. Try one on your own… Suppose an investment of $10,000 doubles in value every 13 years. How much is the investment worth after 52 years? After 65 years? (hint: first write the function and remember it is doubling every 13 years)

13. Homework Page 432-433 #’s 2-22evens