Janine, a science student, measured the volume of carbon dioxide gas that can be absorbed by one cubic centimeter of charcoal at pressure x. She made the following four sets of measurements:

(120, 3.1)

(340, 5.5)

(534, 7.1)

(698, 8.3)

Janine finds that the volume, f(x), to be a function of pressure, x, and decides to use the formula discussed earlier in this project to fit her data. Recall that the formula is:

f(x) = A + B(x – xo) + C(x – xo)(x – x1) + D(x – xo)(x – x1)(x – x2)

where A, B, C, and D are constants, while xo, x1, x2 are the x-coordinates of three of the data

Question

Janine, a science student, measured the volume of carbon dioxide gas that can be absorbed by one cubic centimeter of charcoal at pressure x. She made the following four sets of measurements:

(120, 3.1)

(340, 5.5)

(534, 7.1)

(698, 8.3)

Janine finds that the volume, f(x), to be a function of pressure, x, and decides to use the formula discussed earlier in this project to fit her data. Recall that the formula is:

f(x) = A + B(x – xo) + C(x – xo)(x – x1) + D(x – xo)(x – x1)(x – x2)

where A, B, C, and D are constants, while xo, x1, x2 are the x-coordinates of three of the data