Suppose that for selected years from 1970 to 2006, the following table shows the percent of total U.S. workers who are 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 1970. Find the function that models the instantaneous rate of change of the percent of U.S. workers who are female.

Question

Suppose that for selected years from 1970 to 2006, the following table shows the percent of total U.S. workers who are 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 1970. Find the function that models the instantaneous rate of change of the percent of U.S. workers who are female.
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Quizplus · Accepted Answer

The instantaneous rate of change is given by the derivative of the function. Taking the derivative of p(t), we get:

p'(t) = 0.46t^2 - 13.64t + 111.84

Therefore, the function that models the instantaneous rate of change is p'(t) = 0.46t^2 - 13.64t + 111.84. This matches option C.

Suppose That for Selected Years from 1970 to 2006, the Following