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example 3 Peanut Production Chapter 4.2 Georgia’s production of peanuts has increased moderately in the last 10 years, but profit margins have been reduced by lower prices, declining yields, and increasing costs. The table gives the annual revenue, variable costs, and fixed costs for peanut production in Georgia for the years 1998–2002. 19981999200020012002 Revenue ($) 57,25058,39559,56360,75461,969 Variable Costs ($) 28,06428,90529,77330,66631,586 Fixed Costs ($) 11,38211,72412,07612,43812,811 The function that models the revenue from peanut production in Georgia for the years 1998–2002 is given by where x is number of years after 1990. The function that models the total cost (variable plus fixed) of peanut production in Georgia is given by where x is the number of years after 1990. 2009 PBLPathways

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Georgia’s production of peanuts has increased moderately in the last 10 years, but profit margins have been reduced by lower prices, declining yields, and increasing costs. The table gives the annual revenue, variable costs, and fixed costs for peanut production in Georgia for the years 1998–2002. 19981999200020012002 Revenue ($) 57,25058,39559,56360,75461,969 Variable Costs ($) 28,06428,90529,77330,66631,586 Fixed Costs ($) 11,38211,72412,07612,43812,811 The function that models the revenue from peanut production in Georgia for the years 1998–2002 is given by where x is number of years after 1990. The function that models the total cost (variable plus fixed) of peanut production in Georgia is given by where x is the number of years after 1990.

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2009 PBLPathways a.Write a function P(x) that models the profit from peanut production. b.Graph the functions R, C, and P on the same set of axes. c.What is the slope of the graph of P(x)? Interpret the slope as a rate of change. d.If the model remains accurate, what will be the profit for peanut production in 2010?

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2009 PBLPathways a.Write a function P(x) that models the profit from peanut production. ?

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2009 PBLPathways a.Write a function P(x) that models the profit from peanut production. ?

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2009 PBLPathways a.Write a function P(x) that models the profit from peanut production. ?

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2009 PBLPathways a.Write a function P(x) that models the profit from peanut production. ?

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2009 PBLPathways a.Write a function P(x) that models the profit from peanut production. ?

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2009 PBLPathways a.Write a function P(x) that models the profit from peanut production. ?

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2009 PBLPathways a.Write a function P(x) that models the profit from peanut production. ?

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2009 PBLPathways a.Write a function P(x) that models the profit from peanut production. ?

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2009 PBLPathways a.Write a function P(x) that models the profit from peanut production. ?

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2009 PBLPathways a.Write a function P(x) that models the profit from peanut production. ?

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2009 PBLPathways a.Write a function P(x) that models the profit from peanut production.

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2009 PBLPathways b.Graph the functions R, C, and P on the same set of axes.

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2009 PBLPathways b.Graph the functions R, C, and P on the same set of axes. R(x) C(x) P(x)

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2009 PBLPathways c.What is the slope of the graph of P(x)? Interpret the slope as a rate of change. m = -0.058 b = 18.2812 -0.058 thousand dollars per year or -58 dollars per year

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2009 PBLPathways c.What is the slope of the graph of P(x)? Interpret the slope as a rate of change. m = -0.058 b = 18.2812 -0.058 thousand dollars per year or -58 dollars per year

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2009 PBLPathways c.What is the slope of the graph of P(x)? Interpret the slope as a rate of change. m = -0.058 b = 18.2812 -0.058 thousand dollars per year or -58 dollars per year

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2009 PBLPathways c.What is the slope of the graph of P(x)? Interpret the slope as a rate of change. m = -0.058 b = 18.2812 -0.058 thousand dollars per year or -58 dollars per year

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2009 PBLPathways d.If the model remains accurate, what will be the profit for peanut production in 2010?

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2009 PBLPathways d.If the model remains accurate, what will be the profit for peanut production in 2010?

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2009 PBLPathways d.If the model remains accurate, what will be the profit for peanut production in 2010?

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