The Brazilian Amazon rain forest is the world's largest tropical rain forest, with some of the greatest biodiversity of any region.
In 2012, 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 2012.
Source: Brazil’s National Institute for Space Research
The data in the line graph can be modeled by the following third and fourth-degree polynomial functions:
Amazon rain deforestation, in squire kilometers, x years after 2000 f(x) = 81x3 - 1691x2 + 8120x + 12,465 g(x) = -15x4 + 484x3 - 5155x2 + 19.112x + 2797.
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 Lending Coefficient Test to determine the end behavior to the right for the graph of g behavior to the right for the graph of g
d. Assume that the rate of 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.
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