The Nature of Exponential Growth
- Exponential growth is a pattern of growth in which each term is multiplied by a constant amount (greater than one) to produce the next term
- Graphs of exponential growth functions increase at a constantly increasing rate
- Exponential functions have a repeating pattern of finite differences: the ratio of successive finite differences is constant
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comparing_models_of_growth_homework.pdf | |
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exponential_growth_homework.pdf | |
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Exponential Decay: Connecting to Negative Exponents
- Exponential Decay is a pattern of decay in which each term is multiplied by a constant fraction between zero and one to produce the next term
- Exponential Decay graphs decrease at a constantly decreasing rate
- Half-Life is the length of time for an unstable element to spontaneously decay to one half its original amount
- Doubling time is length of time for an element to double from its original amount.
- Negative exponents in an exponential equation indicate decay, provided the growth rate is a whole number.
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exponential_decay.doc | |
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exponential_decay_homework.pdf | |
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Rational Exponents
- A power involving a rational exponent with numerator 1 and denominator n can be interpreted as the nth root of the base
- You can evaluate a power involving a rational exponent with numerator m and denominator n by taking the nth root of the base raised to the exponent m.
- The exponent rules hold true for powers involving rational exponents
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Solving Exponential Equations
- Exponential equations are equations in which the independent variable is an exponent.
- Exponential equations can be solved by re-writing one, or both sides of the equation in terms of the same base and then equating the exponents creating a linear equation
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Properties of Exponential Functions
- Exponential Functions have equations of the form y = ab^x (where x is an exponent, a is the y-intercept, and b represents the growth or decay rate.
- Depending upon the values of a and b, the exponential function y = ab^x can be either increasing or decreasing
- The exponential function y = ab^x will have a horizontal asymptote at the line y = 0.
- You can write an equation for an exponential function if you are given enough information about its graph or properties.
properties_of_exponential_functions.doc | |
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Transformations of Exponential Functions
transformations_of_exponential_functions.doc | |
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graphing_example_1.pdf | |
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graphing_example_2.pdf | |
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Additional Resources
exponential_functions_review.pdf | |
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exponential_functions_assignment.pdf | |
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