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 points given.
When we use Janine’s data, what would the value of A be?
120
340
5.5
3.1
None of those answers worked when I tried.
It's 3.1
To determine the value of constant A in the formula, we need to substitute the given data points into the equation and solve for A. Let's start with the first data point: (120, 3.1).
Substituting x=120 and f(x)=3.1 into the equation:
3.1 = A + B(120 - xo) + C(120 - xo)(120 - x1) + D(120 - xo)(120 - x1)(120 - x2)
Since we want to find the value of A, we can ignore the terms involving B, C, and D because they do not depend on A. This leaves us with:
3.1 = A
Therefore, the value of A, when using the first data point (120, 3.1), is 3.1.
It seems like none of the given answer options match the value of A in this case. Based on the information provided, it is not possible to determine the exact value of A without further data or clarification.