Burton, Gibson, Huckaby, Molyneaux 1

Longwood University /
MATH 121 Writing Assignment /
Problem #3 /
Cynthia L. Burton, Kevin A. Gibson, Autumn R. Huckaby, & Angela N. Molyneaux /
12/1/2015 /

Deforestation in the Amazon

In this problem we are analyzing the running total amount of deforestation in the Amazon from the year 1990 to 2005. We decided to choose a letter T to represent years since 1990 as our independent variable, and the letter A to represent the total cumulative area of deforestation (in thousands of square kilometers) as our dependent variable. The appropriate scales for the x-axis would be a minimum of 0 representing the year 1990 and a maximum of 35.

The best linear function to fit the data, that we found, was A = 18.998529411765 T + 423.32352941176.

X / y / y line / y – y line / y-yline2
0 / 436 / 423.3235 / 12.6765 / 160.6937
1 / 448 / 442.322 / 5.678 / 32.2397
2 / 461 / 461.3205 / -.3205 / 0.1027
3 / 477 / 480.319 / -3.319 / 11.0158
4 / 492 / 499.3175 / -7.3175 / 53.5458
5 / 521 / 518.316 / 2.684 / 7.2039
6 / 539 / 537.3145 / 1.6855 / 2.8409
7 / 552 / 556.313 / -4.313 / 18.601969
8 / 569 / 575.3115 / -6.3115 / 39.835
9 / 586 / 594.31 / -8.31 / 69.0561
10 / 606 / 613.3085 / -7.3085 / 53.4142
11 / 624 / 632.307 / -8.307 / 69.0062
12 / 649 / 651.3055 / -2.3055 / 5.3153
13 / 674 / 670.304 / 3.696 / 13.6604
14 / 700 / 689.3025 / 10.6975 / 114.4365
15 / 719 / 708.301 / 10.699 / 114.4686

The sum of squares for the linear function is 765.436769.

X / Y / y line / y - y line /
0 / 436 / 443.9755 / 2.0245 / 4.0986
1 / 448 / 448.8609 / -0.8609 / 0.7411
2 / 461 / 464.2568 / -3.2568 / 10.6067
3 / 477 / 480.1808 / -3.1808 / 10.1175
4 / 492 / 496.650996 / -4.650996 / 21.6318
5 / 521 / 513.6861 / 7.3139 / 53.4931
6 / 539 / 531.3056 / 7.6944 / 59.2038
7 / 552 / 549.5293 / 2.4707 / 6.1044
8 / 569 / 568.3782 / 0.6218 / 0.3866
9 / 586 / 587.8736 / -1.8736 / 3.5104
10 / 606 / 608.0376 / -2.0376 / 4.1518
11 / 624 / 628.8933 / -4.8933 / 23.9444
12 / 649 / 650.4644 / -1.4644 / 2.1445
13 / 674 / 672.7753 / 1.2247 / 1.49989
14 / 700 / 695.8515 / 4.1485 / 17.2101
15 / 719 / 719.7192 / -0.7192 / 0.5172

The sum of squares for this exponential function is 208.75519.

The exponential function fits better because it correlates more closely with the thousands of square kilometers of forest lost each year. Based on this Linear Regression model the year 2010 would have had 803.294 thousands of square kilometers of deforestation in total while 2020 should have 993.279.

Following the Exponential Regression model below, 2010 would have lost more with a total of 852.466 thousands of square kilometers of deforestation leading to a new total of 1,194.765 to have been lost by 2020.

When comparing our problem’s source in the book to our own calculations we ran into an issue: There was none since this was a student project. To accommodate for this we used date from “rainforests.mongabay.com.” According to this site the Amazon lost a total of 741.212 thousands of square kilometers. However, it’s important to mention that when comparing this data set to the book’s the total area lost since 1990 was offset by about 30 (Example of total deforestation by 2005  Website: 687,901 sq. km / Book: 719,000 sq. km). The Linear Regression model still had the closer prediction with 803.294 thousands sq. km of deforestation in 2010.

In closing, the exponential function fit well at first with the data given, but when it came to making predictions the linear function was more accurate in calculating the unknown.

Works Cited

  1. Butler, Rhett A. "Calculating Deforestation in the Amazon." Mongabay.com. N.p., 2010-2014. Web. 30 Nov. 2015.