   Chapter 10.5, Problem 43E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# 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 StatisticsAssume that these data can be modeled with the function p ( t ) = 78.6 t + 2090 1.38 t + 64.1 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 lim x → ∞ P ( t ) .(b) Interpret your answer to part (a).(c) Does p(t) have any vertical asymptotes within its domain t ≥ 0 0?(d) Whenever p ( t ) <  0 or  p ( t )   > 100 , the model would be inappropriate. Determine whether the model is ever inappropriate for t ≥ 0 .

(a)

To determine

To calculate: The value of limtP(t), if P(t)=78.6t+20901.38t+64.1.

Explanation

Given Information:

If P(t) is the percent of the U.S. workforce that is female and t is the number of years past 1950, then their relationship is given by,

P(t)=78.6t+20901.38t+64.1

Calculation:

As it is provided that if P(t) is the percent of the U.S. workforce that is female and t is the number of years past 1950, then their relationship is given by,

P(t)=78.6t+20901.38t+64.1

Now, obtain the limit limtP(t) as,

limtP(t)=limt(78.6t+20901.38t+64

(b)

To determine

The interpretation of the answer in part (a) if P(t) is the model P(t)=78.6t+20901.38t+64.1.

(c)

To determine

Whether P(t) has any vertical asymptotes in the domain t0 if P(t)=78.6t+20901.38t+64.1.

(d)

To determine

Whether the model P(t)=78.6t+20901.38t+64.1 is ever inappropriate for t0, where the model is inappropriate when p(t)>0 or p(t)>100.

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