Chapter 9.5, Problem 55E

(a)

To determine

To calculate: The function for the instantaneous rate of change of the percent of U.S. females workers, if the percent function of total U.S. females workers is model as $p\left(t\right)=\frac{78.6t+2090}{1.38t+64.1}$, where t is the number of year past 1950. The data from year 1950 to 2050 from which the percent function is modeled is tabulated below.

Year	% Females	Year	% Females
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

(b)

To determine

To calculate: The instantaneous rates of change of the percent of the U.S. females worker in 2005 and 2020 respectively for the function $p^{\prime }\left(t\right)=\frac{2154.06}{{\left(1.38t+64.1\right)}^2}$.

(c)

To determine

The interpretation of the instantaneous rate of the change of the percent of the U.S. female workers in year 2005 and in year 2020 respectively.