Exponential Functions - Day 1 (Student notes



Review:From previous lessons, name 2 characteristics of an exponential function.1. 39179576200002. Any quantity that grows or decays by a fixed percent at regular intervals is said to have exponential growth or exponential decay.Exploring Exponential Growth and Decay FunctionsGraph the following:469201528575y ?????xy ?????x1.y ? 2x1.y ? 2x2.2.What do you notice about both graphs? Exponential Growth FunctionsExponential Decay Functionsy = a(b)xy = a(b)xWhen and,When and,the graph will be increasing (growing).the graph will be decreasing (Decaying).EXAMPLES685800244475a.00a.402971024447500Tell whether the following graphs represent an exponential growth or Decay.b.Tell whether the following equations represent an exponential growth or Decay.y=32xb. y=0.54xc. y=213x-3175673110The general equation for an exponential GROWTH function is:4464050295910y = a(1 + r)xwhere, (1 + r) = bThe general equation for an exponential DECAY function is:y = a(1 - r)xwhere, ( 1 – r ) = bEXAMPLESIdentify the initial value, the growth or decay factor, and the growth or decay rate of the exponential function.1.y = 3(1.8)x2.y = 2.1 (1.04)xGrowth or decay: GROWTHGrowth or decay Initial value: 3Initial value _______Growth or decay factor: 1.8Growth or decay factor _____________Growth or decay rate: 0.8 or 80%Growth or decay rate _______________3.y = 9 (.8)x4.y = 2 (.94)xGrowth or decay Growth or decay Initial value Initial value Growth or decay factor Growth or decay factor Growth or decay rate Growth or decay rate ................
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