5.1 – Exponential Functions

• 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) = ax

Behavior

• To analyze the behavior of an exponential function, remember…– a-x = 1/(ax)

• For any exponential function with a ≠ 1;– A function is decreasing if 0 < a < 1 – f(x) -> ∞ as x -> - ∞– f(x) -> 0 as x -> ∞

Behavior continued…

• A function is increasing if a > 1– f(x) -> 0 as x -> - ∞– f(x) -> ∞ as x -> ∞

Exponential Equations

• An exponential equation may be written as a function in which variables are exponents– ax = ab

• For us to solve them currently, we will attempt to create common bases

• Example. Solve the exponential function 25x – 125 = 0

• Can we write 25 and 125 as some form of a common base? • Remember! Powers, not multiplication

• Example. Solve the exponential equation 32x-1 = 27

• Example. Solve the exponential equation 2x+1 = 643

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