Algebra II : Interpolations
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Example Questions
Example Question #1 : Interpolations
Given the two following points, use interpolation to determine the best estimate for the value
Using our two known points, we can use interpolation to determine the value at any point between them with the following formula:
Where 
Example Question #1 : Interpolations
The output of a factory in units per day versus the number of employees working is plotted on the graph below, with the following data points collected:
(Workers, Units of output per day):
Assuming a linear relationship, interpolate to find how many units will be made per day if 
We want to do a linear interpolation since the relationship between workers and units can be assumed to be linear. This means there is a constant slope between the points, so the slope between two known points will be equal to the slope between the point we are trying to find and some known point. This is expressed in the relation:
where 
Plugging these into our interpolation formula and knowing 
Simplifying and rearranging to solve for 
So there are 
Example Question #2 : Interpolations
Given the points
Use the formula for interpolation to determine the value of y:
We will use (30, 51) as our x2 and y2 and (20, 36) as our x1 and y1 and we will solve for y using 26.5 for x.
Example Question #1 : Interpolations
Given 
Use the formula for interpolation:
We will use (30, 15) as x2 and y2, (15, 10) as x1 and y1, and solve for y when x=17.9:
Example Question #5 : Interpolations
Mary measures her height every year on her birthday, starting at 11 until she turns 16. She wants to make a table with all the information gathered, but discovers she lost the piece of paper on which she wrote her height down on her 14th birthday. Her incomplete table looks like this:
| Age (years) | Height (inches) |
| 11 | 47.5 |
| 12 | 50.25 |
| 13 | 53 |
| 14 | ? |
| 15 | 58.5 |
| 16 | 61.25 |
Using the method of linear interpolation, which of the following is the closest estimate of Mary's height on her 14th birthday?
Not enough information given in the problem.
Using linear interpolation means that we draw a line between the points on our data set and use that line to estimate a value that lies between two data points; in this case, we have the data from Mary's 13th and 15th birthdays, so we can describe a line between those two points and estimate her height at 14. Our line will be written in slope-intercept form:
Where the variable 
Next, we find the y-intercept by plugging in our slope (which we just found) and a point from our table (we'll stick with 
Simplify:
Subtract 35.75 from both sides to solve for 
The equation of our interpolation line is:
So, to get an estimate of Mary's height on her 14th birthday, we plug in 
Our estimate of Mary's height at 
Example Question #1 : Interpolations
Find the value of 
Write the interpolation formula.
Identify and substitute the values.
Simplify the fraction.
The answer is:
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