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Week 5 Exponential Functions Presentation

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Week 5 6.1 Exponential Functions 3, 13, 23, 33, 63 Exponential Functions NOTE: An exponential growth is the original range (output) increase by the same percentage over equal increments. A linear growth is the original range (output) increasing by the same amount over equal increments found in the domain These functions show exponential growth OR the constant rate of change (a constant number for which the output grows by every input) ● Percentage Change: change based on a percent of the original amount ● Exponential growth: constant increase based on a multiplicative rate over equal increments of time (a percent increase of the original amount over time) ○ EXAMPLE: The population of a colony of birds in 2008 is 43, each year the population increases by 5% ● Exponential Decay: decrease based on a constant multiplicative rate over equal increments of time (percent decrease of the original amount over time) ○ EXAMPLE: A silo of grain is used throughout the year. It starts with 100 gallons of grain and each month is decreased by 8.3% General Form of Exponential Functions For any real number x, f(x) = abx Where: ● ● ● ● ● ● ● ● NOTE: b has to be positive to insure that the equations results in a real number, it also cannot be one because 1 is a constant and would thus result in a straight line with no percentage changes. a is a non-zero real number called the initial value b is any positive real number such that b does not equal 1 Domain of ...
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