The table gives the number of females who earned doctoral degrees in the United States (in thousands) for the years 1997 to 2006. (Source: Statistical Abstract of the United States, 2006)

(a) Plot the data letting $x=7$ represent 1997, $x=8$ represent 1998, and so on.
(b) Find a function of the form $f(x)=a(x-h)^{2}+k$ that models this data. Let $(7,19)$ represent the vertex, and use $(16,27)$ to determine the value of $a$.
(c) Use the statistical capability of a graphing calculator to find the best-fitting quadratic function, $g$, for this data. Graph both functions $g$ and $f$ from part (b) in the same window as the data points.
Which function is the better fit?

Question

The table gives the number of females who earned doctoral degrees in the United States (in thousands) for the years 1997 to 2006. (Source: Statistical Abstract of the United States, 2006)
  
(a) Plot the data letting $x=7$ represent 1997, $x=8$ represent 1998, and so on.
(b) Find a function of the form $f(x)=a(x-h)^{2}+k$ that models this data. Let $(7,19)$ represent the vertex, and use $(16,27)$ to determine the value of $a$.
(c) Use the statistical capability of a graphing calculator to find the best-fitting quadratic function, $g$, for this data. Graph both functions $g$ and $f$ from part (b) in the same window as the data points.
Which function is the better fit?

Quizplus · Accepted Answer

The Answer of The table gives the number of females who earned doctoral degrees in the United States (in thousands) for the years 1997 to 2006. (Source: Statistical Abstract of the United States, 2006)
  
(a) Plot the data letting $x=7$ represent 1997, $x=8$ represent 1998, and so on.
(b) Find a function of the form $f(x)=a(x-h)^{2}+k$ that models this data. Let $(7,19)$ represent the vertex, and use $(16,27)$ to determine the value of $a$.
(c) Use the statistical capability of a graphing calculator to find the best-fitting quadratic function, $g$, for this data. Graph both functions $g$ and $f$ from part (b) in the same window as the data points.
Which function is the better fit?

The Table Gives the Number of Females Who Earned Doctoral x=7x=7x=7

The Table Gives the Number of Females Who Earned Doctoral $x=7$