For selected years from 1950 and with projections to 2050, the table shows the percent of total U.S. workers who were female.

Assume these data can be modeled with the function

where p(t) is the percent of the U.S. workforce that is female and t is the number of years past 1950.
(a) Find the function that models the instantaneous rate of change of the percent of U.S. workers who were female.
(b) Use the function from part (a) to find the instantaneous rates of change in 2005 and in 2020.
(c) Interpret each of the rates of change in part (b).

Transcribed Image Text:

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 46.6 47.7 2000 2050 78.6t + 2090 P(t): 1.38t + 64.1