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# Can you explain what interpolation is and how to use it when asked in an exam question? If you could give an example, that would be great. Thanks!?

Interpolation is a estimation of a value within two known values in a sequence of values. Example If at time = 0s my speed was 0kmh (0s, 0kmh) and at time = 10s my speed was 10kmh (10s, 10kmh), how would you estimate the speed at time = 5s? Well, since we are using those two points, (0, 0) and (10, 10), to estimate the speed in between the points, this would require interpolation. Since 5s is halfway through 0s and 10s, if we devide the duration (10s) in half, we find the speed at 10s. 10kmh / 2 = 5kmh. Extra Info If we wanted to answer this on a graph (assuming constant acceleration), we would draw a line between the two points and find the point half way through. This is called linear interpolation, 'linear' because we are using a line, and it would give us the exact same answer. Notice that we are using two known values (to draw a line) and estimating another value in-between them. There are other types of interpolation, e.g. polynomial interpolation, but for that we need formulas, so I won't open that can of worms for now! Post another question if you have a more specific question in mind.

Mujavid Bukhari
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12k students helped

Maths

3n^2

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