- #1
Shakattack12
- 24
- 2
Homework Statement
The problem involves a population in a country:
year 1930 1940 1950 1960 1970
Pop 1.0 1.2 1.6 2.8 5.4
(millions)
Part A involved finding the population in 1920 using Newton Divided Differences Interpolation (SOLVED)
Part B requires finding the year when the population is 60.4 million. I went through the method below but apparently there is any easier more accurate way (not using a calculator). Please help.
Homework Equations
The equation for the population is:
y = 0.0001x^3 - 0.581x^2 + 1125.22x - 726412.4
The Attempt at a Solution
For part B I used Newtons formula and a divided differences table
Substitute in values using interpolation formula
x = g(y0) + (y-y0)g(y0y1) + (y-y0)(y-y1)g(y0y1y2)
Let y = 60.4
x = g(y0) + (60.4-y0)g(y0y1) + (60.4-y0)(60.4-y1)g(y0y1y2)
let y0 = 50.5125, g(y0) = 2015 …x = 2015 + (60.4-50.5125)x0.447928331 + (60.4-50.5125)(60.4-84)x-0.001538931
x = 2019.787993
This is an approximation. The actual year is 2020.