Chapter 10.5, Problem 43E

Females in the workforce For selected years from 1950 and projected to 2050, the table shows the percent of total U.S. workers who were female.

Year	% Female	Year	% Female
1950	29.6	2010	47.9
1960	33.4	2015	48.3
1970	38.1	2020	48.1
1980	42.5	2030	48.0
1990	45.2	2040	47.9
2000	46.6	2050	47.7

Source: U.S. Bureau of Labor Statistics

Assume that these data can be modeled with the function

$p(t)=\frac{78.6t+2090}{1.38t+64.1}$ where $p\left(t\right)$ is the percent of the U.S. workforce that is female and t is the number of years past 1950.

(a) Find $\underset{x\to \infty }{\lim }P\left(t\right)$.

(b) Interpret your answer to part (a).

(c) Does p(t) have any vertical asymptotes within its domain $t\ge 0$

0?

(d) Whenever $p\left(t\right)<\text{ 0 or }p\left(t\right)>100,$ the model would be inappropriate. Determine whether the model is ever inappropriate for $t\ge 0$.