The data considered here are the population of a country for the years 1 = 1900, 2 = 1910, 3 = 1920, 4 = 1930, ··· , 12 = 2010. The i ’s are the corresponding population values, and they should be...

The data considered here are the population of a country for the years

₁
= 1900,

₂
= 1910,

₃
= 1920,

₄
= 1930, ··· ,

₁₂
= 2010. The


_i
’s are the corresponding population values, and they should be given per million. For example, the population of the USA is given in Table 5.7, and this is from the Wikipedia page Demographics of the United States.

(a) Fit this data with: i) a global polynomial using Lagrange interpolation, and ii) a natural cubic spline. Plot these two curves and the data on the same axis. Make sure to include a legend in your plot.

(b) What do each of the two interpolation functions give as the population in 2005?

(c) What do each of the two interpolation functions predict the population will be in 2015?