1. 5.1 – Exponential Functions

2. Exponential Function = a type of function in which a constant is raised to a variable power Many real-life applications using exponential functions Exponential functions will be of the form : f(x) = a x

3. Behavior To analyze the behavior of an exponential function, remember… – a -x = 1/(a x ) For any exponential function with a ≠ 1; – A function is decreasing if 0 < a < 1 – f(x) -> ∞ as x -> - ∞ – f(x) -> 0 as x -> ∞

4. Behavior continued… A function is increasing if a > 1 – f(x) -> 0 as x -> - ∞ – f(x) -> ∞ as x -> ∞

5. Exponential Equations An exponential equation may be written as a function in which variables are exponents – a x = a b For us to solve them currently, we will attempt to create common bases

6. Example. Solve the exponential function 25 x – 125 = 0 Can we write 25 and 125 as some form of a common base? Remember! Powers, not multiplication

7. Example. Solve the exponential equation 3 2x-1 = 27

8. Example. Solve the exponential equation 2 x+1 = 64 3

9. Assignment Page 384 19, 22, 24, 25, 27, 32, 34, 39, 41, 43