# Math Help - Interpolation

1. ## Interpolation

Hi good morning: I have a question with the following:

In a university in 2002 had 10,400 students enrolled, and 2007, 13200.
Estimating how many there were: 2003, 2005, 2000, 2010 and 2040.

SOLUTION:

For the linear interpolation formula:

$f(x) = f(x_0) + \displaystyle\frac{f(x_1) - f(x _0)}{x_1 - x_0} (x- x_0)$

And replacing the values:

For the year 2003:

$= 10400 + \displaystyle\frac{10400 - 13200}{2007 - 2002} (2003 - 2002)= 9840$

For the year 2005:

$= 10400 + \displaystyle\frac{10400 - 13200}{2007 - 2002} (2005 - 2002) = 8720$

And so on.

But when calculating the year 2040 the output is: $-10880$

Here is my question. Is that correct?

Greetings and apologies if this is not the forum suitable, to me is an ongoing problem of mathematical analysis.

2. Originally Posted by Dogod11
Hi good morning: I have a question with the following:

In a university in 2002 had 10,400 students enrolled, and 2007, 13200.
Estimating how many there were: 2003, 2005, 2000, 2010 and 2040.

SOLUTION:

For the linear interpolation formula:

$f(x) = f(x_0) + \displaystyle\frac{f(x_1) - f(x _0)}{x_1 - x_0} (x- x_0)$

And replacing the values:

For the year 2003:

$= 10400 + \displaystyle\frac{\begin{color}{red}10400 - 13200\end{color}}{2007 - 2002} (2003 - 2002)= 9840$

For the year 2005:

$= 10400 + \displaystyle\frac{\begin{color}{red}10400 - 13200\end{color}}{2007 - 2002} (2005 - 2002) = 8720$

And so on.

But when calculating the year 2040 the output is: $-10880$

Here is my question. Is that correct?

Greetings and apologies if this is not the forum suitable, to me is an ongoing problem of mathematical analysis.
Clearly it can't be. The number of students are on the rise so in 2040, we should have a number well above 13200. I believe your mistake is in red above - the numbers should be switched.

3. Since I could correct, I had invested the terms of the numerator,

A greeting and thanks