   Chapter 13.3, Problem 41E ### 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

# Social Security beneficiaries With data from the Social Security Trustees Report for selected years from 1950 and projected to 2030, the number of Social Security beneficiaries (in millions) can be modeled by B ( t ) =   0.00024 t 3 − 0.026 t 2 +   1.6 t   +   2.2 where t is the number of years past 1950. Use the model to find the average number of Social Security beneficiaries per year (actual and predicted) between(a) 1980 and 2000. (b) 2010 and 2030.

(a)

To determine

To calculate: The average number of Social Security beneficiaries per year between 1980 and 2000 where with the data from the social security Trustees Reports for selected years from 1950 and projected to 2030, the number of Social Security beneficiaries (in millions) can be modeled by B(t)=0.00024t30.026t2+1.6t+2.2 where t is the number of years past 1950.

Explanation

Given information:

It is provided that with the data from the social security Trustees Reports for selected years from 1950 and projected to 2030, the number of Social Security beneficiaries (in millions) can be modeled by B(t)=0.00024t30.026t2+1.6t+2.2 where t is the number of years past 1950.

Formula used:

Average value

The average value of a continuous function y=f(x) over the interval [a,b] is:

Average value=1baabf(x)dx

Calculation:

The provided function is:

B(t)=0.00024t30.026t2+1.6t+2.2

Since, the average number of Social Security beneficiaries per year between 1980 and 2000 is to be determined.

Thus, the interval is [30,50]

Consider the formula:

Average value=1baabf(x)dx

Substitute 50 for b, 30 for a and 0.00024t30.026t2+1.6t+2.2 for f(x) in above equation to get:

Average value=150303050(0.00024t30.026t2+1.6t+2.2)dt=1203050(0.00024t30.026t2+1

(b)

To determine

To calculate: The average number of Social Security beneficiaries per year between 2010 and 2030 where with the data from the social security Trustees Reports for selected years from 1950 and projected to 2030, the number of Social Security beneficiaries (in millions) can be modeled by B(t)=0.00024t30.026t2+1.6t+2.2 where t is the number of years past 1950.

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