1. Exponential Functions An exponential function is represented: F(x) = a b x a = starting amount (when x = 0) b = base that is multiplied. b must be greater than 0 X = the variable in the exponent Exponential Growth: when b > 1 the values get bigger and graph curves up Exponential Decay: when 0 < b < 1 the values get smaller and graph curves down F(x) = 1 (2) x G(x) = 100( ½ ) x Asymptote: An imaginary line where a graph gets flat but Will NEVER touch or cross the line. Pg 26

2. Exponential Examples Evaluate each function at the given value: F(x) = 3 (4) x at x = 5g(x) = 6 (1/2) x at x=3 Y = ½ (4) x y = 5 (2) x The population of mosquitoes in a wetland area can triple every 4 days. If there are 10 mosquitoes to start, how many will there be after 12 days? X -1 0 1 2 3 Y Fill in the table and sketch a graph: X -2 -1 0 1 2 3 Y A fertilizer treatment is applied to a garden. After each month, the strength is ½ of what it was the previous month. If the fertilizer starts at 100% strength, how much is left after 6 months? Days 04812 Mosquitos Pg 27

3. Exponential Vs. Linear pg 31 An EXPONENTIAL function changes with a multiplying/dividing pattern. (factor) A LINEAR function changes with an adding/subtracting pattern. (slope) EXPONENTIAL (multiply) LINEAR (add) Y = a (b) X Y = m X + b a = start value b = factor b = start value m = slope X 0 1 2 3 4 Y 4 8 16 32 64 X 0 1 2 3 4 Y 4 6 8 10 12 Start at 4 Pattern:Multiply by 2 Start at 4 Pattern: Add 2 Y = 4 (2) X Y = 2x + 4 Joe has 50 candies. He eats 10% of the candy each period. How many does he have left at lunch? Joe has 50 candies. He eats 10 pieces of candy each period. How many does he have left at lunch?