Question

Consider the following factors.

1. (FIP,21.00\%,34)
2. (A/G,21.00%,45)
Find the numerical values of the factors using linear interpolation

Answer 1

The numerical values of the factors for the given data points (FIP, 21.00%, 34) and (A/G, 21.00%, 45) using linear interpolation are:

1. For FIP: 21.00% + [(34 - 21) / (45 - 34)] * (21.00% - 21.00%) = 21.00%.

2. For A/G: 21.00% + [(45 - 34) / (45 - 34)] * (21.00% - 21.00%) = 21.00%.

Step-by-step explanation:

Linear interpolation is a method used to estimate values between two known data points. In this case, we have two data points: (FIP, 21.00%, 34) and (A/G, 21.00%, 45). The formula for linear interpolation is:

`\[ \text{Interpolated Value} = \text{Known Value at Lower Point} + \left( \frac{\text{Difference in X Values}}{\text{Difference in X Values between Data Points}} \right) * \left( \text{Difference in Y Values} \right) \]`

For FIP:

`\[ \text{FIP} = 21.00\% + \left( (34 - 21)/(45 - 34) \right) * (21.00\% - 21.00\%) = 21.00\% \]`

For A/G:

`\[ \text{A/G} = 21.00\% + \left( (45 - 34)/(45 - 34) \right) * (21.00\% - 21.00\%) = 21.00\% \]`

In both cases, the interpolated values turn out to be 21.00%, indicating that the linear interpolation method estimates the values at the given data points.

Linear interpolation assumes a straight-line relationship between data points, making it a simple and useful method for estimating values within a given range.