## Related questions with answers

Population Statistics The table shows the life expectancy of a child (at birth) in the United States for selected years from 1920 to 2000. (Source: U.S. National Center for Health Statistics, U.S. Census Bureau)

$\begin{array}{|c|c|} \hline \text { Year, } t & \text { Life expectancy, } y \\ \hline 1920 & 54.1 \\ 1930 & 59.7 \\ 1940 & 62.9 \\ 1950 & 68.2 \\ 1960 & 69.7 \\ 1970 & 70.8 \\ 1980 & 73.7 \\ 1990 & 75.4 \\ 2000 & 77.1 \\ \hline \end{array}$

A model for the life expectancy during this period is

$y=-0.0025 t^2+0.572 t+44.31$

where $y$ represents the life expectancy and $t$ is the time in years, with $t=20$ corresponding to 1920 .

Use the graph of the model to estimate the life expectancy of a child for the years 2005 and 2010.

Solution

VerifiedFirstly, we need to find $t$ that correspondents for the years $2005$ and for $2010$.

Since $t=20$ correspondents to $1920$

$t_{2005}=2005-(1920-200)=105$

$t_{2010}=2010-(1920-200)=110$

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