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Graphing Exponentials and Logs
Day 2 Graphing Exponentials and Logs
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An exponential function is a function with the general form of:
y = abx where x is a real number, a ≠ 0, b > 0, and b ≠ 1.
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Graphing Exponential Equations
y = 2x x y -3 -2 -1 1 2 3
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initial amount growth factor (1+r)
EXPONENTIAL GROWTH y = a • bx time initial amount growth factor (1+r) Ex. The population of the US in 1994 was about 260 million with an average annual rate of increase of about 0.7%. 1. Write a function to model this population. 2. What was the population in 2006?
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Modeling growth The bear population increases at a rate
of 2% per year. There are 1573 bears this year. Write a function that models the bear population. How many bears will there be in 10 years?
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Exponential Decay: y = a(1-r)t
Suppose you want to buy a used car that costs $11,800. The expected depreciation of the car is 20% per year. Estimate the depreciated value of the car after 6 years.
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More Decay….. The population of a certain animal species decreases at a rate of 3.5% per year. You have counted 80 animals in the habitat. Write the equation.
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Ex: Analyzing a Function
Without graphing, determine whether the function y = 14(0.95)x represents exponential growth or exponential decay. Without graphing, determine whether the function y = 0.2(5)x represents exponential growth or exponential decay.
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Graphing Exponential Decay
y = 24(1/3)x Horizontal Asymptote Domain Range x y -3 -2 -1 1 2 3
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Graphing Exponential Decay
y = 100(0.1)x Horizontal asymptote Domain Range x y -3 -2 -1 1 2 3
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Graph and give asymptote, domain and range.
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Translating y = abx y =8(1/2)x y = 8(1/2)x+2 +3
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Translating y = abx y =2(3)x-1 + 1 y = -3(4)x+1 +2
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Homework Pg. 296 (1-14, 29-34)
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