The Brazilian Amazon rain forest is the world’s largest tropical rain forest, with some of the greatest biodiversity of any region. In 2009, the number of trees cut down in the Amazon dropped to its lowest level in 20 years. The line graph shows the number of square kilometers cleared from 2001 through 2009. The data in the line graph can be modeled by the following third- and fourth-degree polynomial functions: a. Use the Leading Coefficient Test to determine the end behavior to the right for the graph of f. b. Assume that the rate at which the Amazon rain forest is being cut down continues to decline. Based on your answer to part (a), will f be useful in modeling Amazon deforestation over an extended period of time? Explain your answer. c. Use the Leading Coefficient Test to determine the end behavior to the right for the graph of g d. Assume that the rate at which the Amazon rain forest is being cut down continues to decline. Based on your answer to part (c), will g be useful in modeling Amazon deforestation over an extended period of time? Explain your answer.
The Brazilian Amazon rain forest is the world’s largest tropical rain forest, with some of the greatest biodiversity of any region. In 2009, the number of trees cut down in the Amazon dropped to its lowest level in 20 years. The line graph shows the number of square kilometers cleared from 2001 through 2009. The data in the line graph can be modeled by the following third- and fourth-degree polynomial functions: a. Use the Leading Coefficient Test to determine the end behavior to the right for the graph of f. b. Assume that the rate at which the Amazon rain forest is being cut down continues to decline. Based on your answer to part (a), will f be useful in modeling Amazon deforestation over an extended period of time? Explain your answer. c. Use the Leading Coefficient Test to determine the end behavior to the right for the graph of g d. Assume that the rate at which the Amazon rain forest is being cut down continues to decline. Based on your answer to part (c), will g be useful in modeling Amazon deforestation over an extended period of time? Explain your answer.
Solution Summary: The author analyzes whether the provided polynomial function f(x) is useful in modeling Amazon deforestation over an extended period of time.
The Brazilian Amazon rain forest is the world’s largest tropical rain forest, with some of the greatest biodiversity of any region. In 2009, the number of trees cut down in the Amazon dropped to its lowest level in 20 years. The line graph shows the number of square kilometers cleared from 2001 through 2009.
The data in the line graph can be modeled by the following third- and fourth-degree polynomial functions:
a. Use the Leading Coefficient Test to determine the end behavior to the right for the graph of f.
b. Assume that the rate at which the Amazon rain forest is being cut down continues to decline. Based on your answer to part (a), will f be useful in modeling Amazon deforestation over an extended period of time? Explain your answer.
c. Use the Leading Coefficient Test to determine the end behavior to the right for the graph of g
d. Assume that the rate at which the Amazon rain forest is being cut down continues to decline. Based on your answer to part (c), will g be useful in modeling Amazon deforestation over an extended period of time? Explain your answer.
Find a polynomial whose graph fits the following points:
(-2,-13), (0,1), (2,3), (4,5)
The population of a certain country was approximately 50 million in 1900, 225 million in 1950, and 350 million in 2000. Construct a model for this data by finding a quadratic equation whose graph passes through the points (0,50), (50,225), and (100,350). Use this model to
estimate the population in 2050.
Let x be the number of years since 1900 and y be the population in millions.
y =
(Use integers or decimals for any numbers in the expression.)
According to the model, what will the population be in the year 2050?
million
y =
-C
The population of a certain country was approximately 75 million in 1900, 175 million in 1950, and 375 million in 2000. Construct a model for this data by finding a quadratic equation whose graph passes through the points (0,75), (50,175), and (100,375). Use this model to
estimate the population in 2050.
Let x be the number of years since 1900 and y be the population in millions.
y=
(Use integers or decimals for any numbers in the expression.)
According to the model, what will the population be in the year 2050?
million
y =
C
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