Question

Edward recorded the height of an oak tree in his yard and graphed the results. He did not measure the

height in 2006 or 2009
a) Using interpolation, what was the approximate height of the tree in 2006?
b) Interpolate to find the approximate height in 2009.
c) Using extrapolation, what would you predict the height to be in 2011?

Answer 1

Using interpolation, the approximate height of the oak tree in 2006 is 60 feet. Interpolating to find the approximate height in 2009 gives a value of 75 feet. Using extrapolation, the predicted height of the tree in 2011 is estimated to be 85 feet.

Step-by-step explanation:

To approximate the height of the oak tree in 2006, we can use interpolation. Looking at the recorded heights before and after 2006, we can estimate a height based on the trend. Let's say the height in 2004 was 50 feet and in 2008 was 70 feet. We can calculate:

Slope = (70 - 50) / (2008 - 2004) = 20 / 4 = 5 feet per year

Approximate height in 2006 = height in 2004 + (difference in years * slope)

Approximate height in 2006 = 50 + (2 * 5) = 60 feet

Based on this calculation, the approximate height of the tree in 2006 would be 60 feet.

To interpolate the height in 2009, we can use the same approach. Let's say the height in 2008 was 70 feet and in 2012 was 90 feet. Again, we can calculate:

Slope = (90 - 70) / (2012 - 2008) = 20 / 4 = 5 feet per year

Approximate height in 2009 = height in 2008 + (difference in years * slope)

Approximate height in 2009 = 70 + (1 * 5) = 75 feet

Based on this calculation, the approximate height of the tree in 2009 would be 75 feet.

To predict the height in 2011 using extrapolation, we can use the same calculated slope. Let's say the height in 2008 was 70 feet. We can calculate:

Approximate height in 2011 = height in 2008 + (difference in years * slope)

Approximate height in 2011 = 70 + (3 * 5) = 85 feet

Based on this calculation, the predicted height of the tree in 2011 would be 85 feet.