Chapter 1.2, Problem 25E

To determine

To use:the data in the table to model the population of the world in the 20^th century by a cubic function. Then use this model to estimate the population in the year 1925.

Answer to Problem 25E

1958 million people.

Explanation of Solution

Given:

The given table is:

Year	Population (millions)	Year	Population (millions)
$1900$	$1650$	$1960$	$3040$
$1910$	$1750$	$1970$	$3710$
$1920$	$1860$	$1980$	$4450$
$1930$	$2070$	$1990$	$5280$
$1940$	$2300$	$2000$	$6080$
$1950$	$2560$

Calculation:

Use technology to plot given points, and use cubic regression tools to graph a curve.

The graph is:

  

The equation of regression curve is $y=0.00129371x^3-7.06142x^2+12823x-7743800$ .

Substitute $x=1925$ to find the required population.

Therefore, $y=0.00129371{\left(1925\right)}^3-7.06142{\left(1925\right)}^2+12823\left(1925\right)-7743800\approx 1958.441$

Thus, the approximation population in the year 1925 is around 1958 million people.