The California Mathematics Content Standards -Grade8 9 10 11 12 

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Algebra II

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Standard 12. Students know the laws of exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay.

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Skills (Note: none listed for science standards)

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Teacher Strategy Describe exponential functions as a function whose general equation is y =a x bx where a and b stand for constants,b is positive,and x and y are independent and dependent variables, respectively.  Exponential functions can be used to represent situations that involve growth or decay, appreciation or depreciation,so they are often very useful as mathematical models in science, business,banking and economics.  Explain that there is a relationship between geometric sequences and exponential functions that is similar to the relationship between arithmetic sequences and linear functions.

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Student Tasks or Scientific Investigation/Experimentation

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Assessment or Scientific Application/Assessment Use a graphing calculator to produce the following: Suppose the annual fees for attending a campus of the California State University system were $700 in 1986 and the cost increased by 10%each year (round answers to the nearest dollar). a)Calculate the cost for the year 1998. b)What would you expect the cost to be four years from 1998? c)What was the cost in 1982? d)Write an equation to describe this situation. e)Sketch a graph of this function from 1986 to 2000. f)In 1994,what were the actual fees?Locate this point in relation to your graphs.Is your model reasonable?Explain.

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Resources and Technology Resource:Exploring Functions with the TI-82 Graphics Calculator by Brendan Kelly. Technology:Quadratic Equations III,Intellectual Software (IS),Division of Queue,Inc.,338 Commerce Drive,Fairfield,CT 06430.

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This page is taken from the Santa Clara Office of Education.

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