Suppose a scientist measures how the volume of an object changes. She records volumes vi at times ti. She would then like to plot a graph showing the process-this would be more illustrative than just a table of numbers. Thus, she needs a function that represents the data. There are many ways to ﬁnd this function; among the available methods are interpolation and approximation. When we interpolate, we want a function that matches the data exactly; when we approximate, we just want to capture the behavior of the data.