Chapter 2, Problem 68RE

Average annual wage The tables below give Social Security Administration data for the U.S. average annual wage from $2011$ and projected to $2021$ and for selected years from $2012$ and projected to $2050$.

(a) Make a scatter plot of each of these data sets with $x$ as the number of years past $2010$.

(b) Decide which one function type could be used as a model for both data sets and find the two models. Let $a(x)$ be the model for the data to $2021$ and $A(x)$ be the model for data to $2050$. Report both models with $4$ significant digit coefficients.

(c) How well do the reported models agree for the data points for $2020$ and $2050$?

(d) When does each reported model predict that the average annual wage will reach $\$150,000$?

Data to 2021 (in dollars)

$\begin{array}{lllll}Year\hfill & 2011\hfill & 2012\hfill & 2013\hfill & 2014\hfill \\ Wage\hfill & 43,009\hfill & 44,644\hfill & 46,496\hfill & 48,595\hfill \end{array}$

$\begin{array}{lllll}Year\hfill & 2015\hfill & 2016\hfill & 2017\hfill & 2018\hfill \\ Wage\hfill & 50,893\hfill & 53,317\hfill & 55,989\hfill & 58,698\hfill \end{array}$

$\begin{array}{llll}Year\hfill & 2019\hfill & 2020\hfill & 2021\hfill \\ Wage\hfill & 61,179\hfill & 63,676\hfill & 66,616\hfill \end{array}$

Data to 2050 (in thousands of dollars)

$\begin{array}{lllll}Year\hfill & 2012\hfill & 2014\hfill & 2016\hfill & 2018\hfill \\ Wage\hfill & 44.6\hfill & 48.6\hfill & 53.3\hfill & 58.7\hfill \end{array}$

$\begin{array}{llll}Year\hfill & 2040\hfill & 2045\hfill & 2050\hfill \\ Wage\hfill & 137.6\hfill & 167.1\hfill & 202.5\hfill \end{array}$

$\begin{array}{lllll}Year\hfill & 2020\hfill & 2025\hfill & 2030\hfill & 2035\hfill \\ Wage\hfill & 63.7\hfill & 76.8\hfill & 93.2\hfill & 113.2\hfill \end{array}$

$41.$

Population of females under $18$

Using U.S. Census Bureau projections from $2020$ to $2060$, the number of U.S. females under the age of $18$, millions, can be modeled by the function

$N=0.150x+37.4$

Where x is the number of the years after $2020.$

Use a graphing calculator to graph this equation for the rang $x-\min =0,x-\max =40,N-\min =35,N-\max =45.$

The point $(20,40.4)$ lies on the graph of this equation. Explain its meaning.

What does the model predict the population of females under $18$ will be in $2030?$

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