Area Between 2 Curves Mini Project

Anna, Rachel, Meredith, Swarangi, 3rd Period

Puerto Rico

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Point of intersection: (8.15, 1.76)

Because we subtracted another part on the side, there is only one point of intersection between the top and bottom equations.

Data Points Used for Top Curve

(0.01, 2.67)

(0.60, 3.07)

(0.81, 3.62)

(1.44, 3.51)

(1.95, 3.48)

(2.34, 3.53)

(2.84, 3.38)

(3.44, 3.46)

(4.10, 3.27)

(4.52, 3.47)

(5.37, 3.31)

(5.95, 3.25)

(6.30, 3.20)

(6.86, 3.16)

(7.52, 2.96)

(8.09, 2.35)

(8.15, 1.76)

Data Points Used for Bottom Curve

(0.18, 0.15)

(0.70, 0.16)

(1.50, 0.15)

(2.18, .024)

(2.68, 0.43)

(3.24, 0.31)

(4.22, 0.24)

(4.95, 0.13)

(5.76, 0.19)

(6.07, 0.20)

(6.82, 0.40)

(7.03, 0.59)

(7.23, 0.84)

(7.41, 1.11)

(7.53, 1.50)

(8.15, 1.76)

Data Points Used for Side Curve

This is the second equation we used to subtract from the top curve.


Another thing to note is that we turned our graph sideways for this (inverted the X and Y values) to make it pass the vertical line test and be a true function. The points listed below have been inverted.


(0.00, 0.03)

(0.44, 0.18)

(0.76, 0.47)

(1.00, 0.60)

(1.35, 0.44)

(1.69, 0.36)

(2.04, 0.28)

(0.30, 2.48)

Equation Used for Top Curve

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Equation Used for Bottom Curve

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Equation Used for Side Curve

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Calculus

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We chose the number 105 as the denominator of the scale factor because that is the actual length of the island.

Answer

The final area we found was 3,840.45 square miles.

Actual Area

The actual area of Puerto Rico is 3,515 square miles.


This leaves us with a 9.3% error.


http://www.nationsencyclopedia.com/economies/Americas/Puerto-Rico.html