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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Vital Statistics The rate of increase of the number of working married couples M (in millions) in the United States from 2008 through 2014 can be modeled by

d M d t = 0.0918 t 2 1.988 t + 10.28 where t is the time in years, with t = 8 corresponding to 2008. The number of working married couples in 2014 was 31.7 million. (Source: U.S. Census Bureau)

(a) Find the model for the number of working married couples in the United States.

(b) Use the model to predict the number of working married couples in the United States in 2019. Does your answer seem reasonable? Explain your reasoning.

(a)

To determine

To calculate: The model for the number of working married couples in the United States whose rate of increase of the number of married couples M (in millions) is dMdt=0.0918t21.988t+10.28 where t is the time in years.

Explanation

Given Information:

The provided model for rate of increase of the number of working married couples is dMdt=0.0918t21.988t+10.28 and the number of working married couples in 2014 was 31.7 million where the corresponding time for year 2008 is t=8.

Formula used:

The sum rule of basic integration [f(x)+g(x)]dx=f(x)dx+g(x)dx.

The simple power rule of integration xndx=xn+1n+1+C.

Calculation:

Consider the provided model for rate of increase of the number of working married couples is dMdt=0.0918t21.988t+10.28.

Integrate the provided model, use the sum rule of basic integration [f(x)+g(x)]dx=f(x)dx+g(x)dx.

dMdtdt=(0.0918t21.988t+10.28)dtM(t)=0.0918t2dt1.988tdt+10.28dt

Integrate further, use the simple power rule of integration xndx=xn+1n+1+C

(b)

To determine

To calculate: The prediction of the number of working married couples in the united states in year 2019 with reason.

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