Chapter 1.4, Problem 53E

LIFE SCIENCE APPLICATIONS

Gender Ratio The number of males per $100$ females, age $65$ or over, in the United States for some recent years is shown in the following table. Source: The U.S Census Bureau.

Year	Males per 100 Females
$1960$	$82.8$
$1970$	$72.1$
$1980$	$67.6$
$1990$	$67.2$
$2000$	$70.0$
$2010$	$77.0$

a. Plot the data, letting $x$ be the years since $1900$.

b. Would a linear or quadratic function best model this data? Explain.

c. If your graphing calculator has a quadratic regression feature, find the quadratic function that best fits the data. Graph this function on the same calculator window as the data. (See Example 7(c).)

d. Choose the lowest point in the table above as the vertex and (110,77.0) as a second point to find a quadratic function defined by $f\left(x\right)=a{\left(x-h\right)}^2+k$ that models the data.

e. Graph the function from part d on the same calculator window as the data and function from part c. Do the graphs of the two functions differ by much?

f. Predict the number of males per $100$ females in $2004$ using the two functions from parts c and d, and compare with the actual figure of $71.7$.