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5.1 – Exponential Functions
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• 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
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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 -> ∞
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Behavior continued…
• A function is increasing if a > 1– f(x) -> 0 as x -> - ∞– f(x) -> ∞ as x -> ∞
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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
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• 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
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• Example. Solve the exponential equation 32x-1 = 27
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• Example. Solve the exponential equation 2x+1 = 643
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• Assignment• Page 384• 19, 22, 24, 25, 27, 32, 34, 39, 41, 43