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Mathematical Applications for the ...

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

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BuyFindarrow_forward

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 Statistics

Assume 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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Chapter 10 Solutions

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Sect-10.1 P-7ESect-10.1 P-8ESect-10.1 P-9ESect-10.1 P-10ESect-10.1 P-11ESect-10.1 P-12ESect-10.1 P-13ESect-10.1 P-14ESect-10.1 P-15ESect-10.1 P-16ESect-10.1 P-17ESect-10.1 P-18ESect-10.1 P-19ESect-10.1 P-20ESect-10.1 P-21ESect-10.1 P-22ESect-10.1 P-23ESect-10.1 P-24ESect-10.1 P-25ESect-10.1 P-26ESect-10.1 P-27ESect-10.1 P-28ESect-10.1 P-29ESect-10.1 P-30ESect-10.1 P-31ESect-10.1 P-32ESect-10.1 P-33ESect-10.1 P-34ESect-10.1 P-35ESect-10.1 P-36ESect-10.1 P-37ESect-10.1 P-38ESect-10.1 P-39ESect-10.1 P-40ESect-10.1 P-41ESect-10.1 P-42ESect-10.1 P-43ESect-10.1 P-44ESect-10.1 P-45ESect-10.1 P-46ESect-10.1 P-47ESect-10.1 P-48ESect-10.1 P-49ESect-10.1 P-50ESect-10.1 P-51ESect-10.1 P-52ESect-10.1 P-53ESect-10.1 P-54ESect-10.1 P-55ESect-10.1 P-56ESect-10.1 P-57ESect-10.1 P-58ESect-10.1 P-59ESect-10.1 P-60ESect-10.1 P-61ESect-10.1 P-62ESect-10.1 P-63ESect-10.1 P-64ESect-10.1 P-65ESect-10.2 P-1CPSect-10.2 P-2CPSect-10.2 P-3CPSect-10.2 P-4CPSect-10.2 P-1ESect-10.2 P-2ESect-10.2 P-3ESect-10.2 P-4ESect-10.2 P-5ESect-10.2 P-6ESect-10.2 P-7ESect-10.2 P-8ESect-10.2 P-9ESect-10.2 P-10ESect-10.2 P-11ESect-10.2 P-12ESect-10.2 P-13ESect-10.2 P-14ESect-10.2 P-15ESect-10.2 P-16ESect-10.2 P-17ESect-10.2 P-18ESect-10.2 P-19ESect-10.2 P-20ESect-10.2 P-21ESect-10.2 P-22ESect-10.2 P-23ESect-10.2 P-24ESect-10.2 P-25ESect-10.2 P-26ESect-10.2 P-27ESect-10.2 P-28ESect-10.2 P-29ESect-10.2 P-30ESect-10.2 P-31ESect-10.2 P-32ESect-10.2 P-33ESect-10.2 P-34ESect-10.2 P-35ESect-10.2 P-36ESect-10.2 P-37ESect-10.2 P-38ESect-10.2 P-39ESect-10.3 P-1CPSect-10.3 P-2CPSect-10.3 P-3CPSect-10.3 P-4CPSect-10.3 P-1ESect-10.3 P-2ESect-10.3 P-3ESect-10.3 P-5ESect-10.3 P-6ESect-10.3 P-7ESect-10.3 P-8ESect-10.3 P-9ESect-10.3 P-10ESect-10.3 P-11ESect-10.3 P-12ESect-10.3 P-13ESect-10.3 P-14ESect-10.3 P-15ESect-10.3 P-16ESect-10.3 P-17ESect-10.3 P-18ESect-10.3 P-19ESect-10.3 P-20ESect-10.3 P-21ESect-10.3 P-22ESect-10.3 P-23ESect-10.3 P-24ESect-10.3 P-25ESect-10.3 P-26ESect-10.3 P-27ESect-10.3 P-28ESect-10.3 P-29ESect-10.3 P-30ESect-10.3 P-33ESect-10.3 P-34ESect-10.3 P-35ESect-10.3 P-36ESect-10.3 P-37ESect-10.3 P-38ESect-10.3 P-39ESect-10.3 P-40ESect-10.3 P-41ESect-10.3 P-42ESect-10.3 P-43ESect-10.3 P-47ESect-10.3 P-48ESect-10.3 P-49ESect-10.4 P-1CPSect-10.4 P-2CPSect-10.4 P-3CPSect-10.4 P-1ESect-10.4 P-2ESect-10.4 P-3ESect-10.4 P-4ESect-10.4 P-5ESect-10.4 P-6ESect-10.4 P-7ESect-10.4 P-8ESect-10.4 P-9ESect-10.4 P-10ESect-10.4 P-11ESect-10.4 P-12ESect-10.4 P-13ESect-10.4 P-14ESect-10.4 P-15ESect-10.4 P-16ESect-10.4 P-17ESect-10.4 P-18ESect-10.4 P-19ESect-10.4 P-20ESect-10.4 P-21ESect-10.4 P-22ESect-10.4 P-23ESect-10.4 P-24ESect-10.4 P-25ESect-10.4 P-26ESect-10.4 P-27ESect-10.4 P-28ESect-10.4 P-29ESect-10.4 P-30ESect-10.4 P-31ESect-10.4 P-32ESect-10.4 P-33ESect-10.5 P-1CPSect-10.5 P-2CPSect-10.5 P-1ESect-10.5 P-2ESect-10.5 P-3ESect-10.5 P-4ESect-10.5 P-5ESect-10.5 P-6ESect-10.5 P-7ESect-10.5 P-8ESect-10.5 P-9ESect-10.5 P-10ESect-10.5 P-11ESect-10.5 P-12ESect-10.5 P-13ESect-10.5 P-14ESect-10.5 P-15ESect-10.5 P-16ESect-10.5 P-17ESect-10.5 P-18ESect-10.5 P-19ESect-10.5 P-20ESect-10.5 P-21ESect-10.5 P-22ESect-10.5 P-23ESect-10.5 P-24ESect-10.5 P-25ESect-10.5 P-26ESect-10.5 P-27ESect-10.5 P-28ESect-10.5 P-29ESect-10.5 P-30ESect-10.5 P-31ESect-10.5 P-32ESect-10.5 P-33ESect-10.5 P-34ESect-10.5 P-35ESect-10.5 P-36ESect-10.5 P-37ESect-10.5 P-38ESect-10.5 P-39ESect-10.5 P-40ESect-10.5 P-41ESect-10.5 P-42ESect-10.5 P-43ECh-10 P-1RECh-10 P-2RECh-10 P-3RECh-10 P-4RECh-10 P-5RECh-10 P-6RECh-10 P-7RECh-10 P-8RECh-10 P-9RECh-10 P-10RECh-10 P-11RECh-10 P-12RECh-10 P-13RECh-10 P-14RECh-10 P-15RECh-10 P-16RECh-10 P-17RECh-10 P-18RECh-10 P-19RECh-10 P-20RECh-10 P-21RECh-10 P-22RECh-10 P-23RECh-10 P-24RECh-10 P-25RECh-10 P-26RECh-10 P-27RECh-10 P-28RECh-10 P-29RECh-10 P-30RECh-10 P-31RECh-10 P-32RECh-10 P-33RECh-10 P-34RECh-10 P-35RECh-10 P-36RECh-10 P-37RECh-10 P-38RECh-10 P-39RECh-10 P-40RECh-10 P-41RECh-10 P-42RECh-10 P-43RECh-10 P-44RECh-10 P-45RECh-10 P-46RECh-10 P-47RECh-10 P-48RECh-10 P-49RECh-10 P-50RECh-10 P-51RECh-10 P-52RECh-10 P-53RECh-10 P-54RECh-10 P-55RECh-10 P-1TCh-10 P-2TCh-10 P-3TCh-10 P-4TCh-10 P-5TCh-10 P-6TCh-10 P-7TCh-10 P-8TCh-10 P-9TCh-10 P-10TCh-10 P-11TCh-10 P-12TCh-10 P-13TCh-10 P-14TCh-10 P-15TCh-10 P-16TCh-10 P-17T

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