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example 3. Peanut Production. Chapter 4.2.

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Example 3

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.

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


Example 3

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.

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.


Example 3

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

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

What is the slope of the graph of P(x)?Interpret the slope as a rate of change.

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


Example 3

?

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


Example 3

?

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


Example 3

?

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


Example 3

?

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


Example 3

?

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


Example 3

?

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


Example 3

?

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


Example 3

?

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


Example 3

?

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


Example 3

?

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


Example 3

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


Example 3

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


Example 3

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

R(x)

C(x)

P(x)


Example 3

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


Example 3

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


Example 3

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


Example 3

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


Example 3

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


Example 3

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


Example 3

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


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