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Doing an assignment and got up to this question "Is is sensible to extrapolate the graph back to the moment when the population was zero? Explain" Don't know how to answer it because I do not know what this word means

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  • $\begingroup$ Continue the image of the graph in its most natural pattern so that the graph now extends to where y (assuming the y axis represents population) is zero $\endgroup$
    – JessicaK
    Mar 9, 2015 at 7:40
  • $\begingroup$ by graph do you mean line? the population starts at 1 so I am guwaaing th answers would be no $\endgroup$
    – Ray Kay
    Mar 9, 2015 at 7:42
  • $\begingroup$ Yes the line. Presumably this is a graph of population vs time. So as time progresses, the population changes, if you use this pattern to guess what the graph "should" look like, does the line you filled in make sense if you try to "go back in time" to the point when the population was zero? $\endgroup$
    – JessicaK
    Mar 9, 2015 at 7:45

2 Answers 2

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Images are always very easy to understand.

enter image description here

When you have a set of data, you can either interpolate data within those points or extrapolate data that lies beyond. If x in this graph represents time, then predicting any associated y before the first point or after the last point would be extrapolating it.

Mathematically speaking, it's practically the same as interpolation, but since it isn't bounded on both sides by data, it may be less reliable. Although, that does not answer the question of whether it is sensible or not in your particular case.

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If the unknown word is "extrapolation"

Suppose that you have a guess about the law governing the behavior of a function acting on elements of an ordered set. Also, suppose that you know a set of pairs of corresponding inputs and outputs. Then, based on your guess you can find or discover new input output pairs. If the new input, as a member of the ordered set is between some old inputs then you interpolate, if it is out somewhere then you extrapolate.

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