From the following data, calculate the population in the year 1985:
| Year | Population (in , 000) |
| 1971 | 12 |
| 1981 | 15 |
| 1991 | 20 |
| 2001 | 27 |
| 2011 | 49 |
To estimate the population in 1985 using numerical analysis, we can apply the method of interpolation, since the year 1985 lies between 1981 and 1991. The data points closest to 1985 are (1981, 15) and (1991, 20). Linear interpolation is a suitable approach for a first approximation. The linear interpolation formula is $$ ____ ________ _____ _________ ________ ________ _________.
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iv) The numerical method:
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v) The method:
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