Chapter 8.4, Problem 84PE

The rural and urban populations in the South (in the United States) between the years 1900 and 1970 can be modeled by the following:

$r\left(t\right)=-3.497t^2+266.2t+20,220$

$u\left(t\right)=0.0566t^3+0.952t^2+177.8t+4593$

The variable t represents the number of years since 1900, $r\left(t\right)$ represents the rural population in thousands, and $u\left(t\right)$ represents the urban population in thousands.

a. Find the function defined by $T\left(t\right)=+r\left(t\right)+t\left(t\right).$ What does $T\left(t\right)$ represent in the context of this problem?

b. Use the function T to approximate the total population in the South for the year 1940.