Answer
See below:
Work Step by Step
(a)
Consider the given function:
$M\left( x \right)=mx+b$
Here, $m$is the slope of the curve made by the given function, $b$is they–intercept, and x is the variable that represents the year after 1980.
The coordinates of the initial and final ends of the line for men shown, respectively, by the red voice balloons are
$\begin{align}
& \left( {{x}_{1}},{{y}_{1}} \right)=\left( 1980,470 \right) \\
& \left( {{x}_{2}},{{y}_{2}} \right)=\left( 2010,710 \right)
\end{align}$
Here, the above values are obtained from the given graph.
Consider the equation for the slope of the line:
$m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$
Substitute the values in the above equation:
$\begin{align}
& m=\frac{710-470}{2010-1980} \\
& =\frac{240}{30} \\
& =8
\end{align}$
The red-colored curve on the given graph starts from a point having the coordinate$\left( 1980,470 \right)$.
The graph has the x-coordinate at the origin as 1980. The y-intercept of the line represents the value of the y-coordinate when the x-coordinate is at the origin. This shows that the y-intercept of the line is 470, which implies$b=470$.
Substitute the values in the given function:
$M\left( x \right)=8x+470$
Thus, the function that models the number of the bachelor’s degree awarded to men is$M\left( x \right)=8x+470$.
(b)
The function $M\left( x \right)=8x+470$ that models the number of the bachelor’s degree awarded to men as calculated in part (a).
The value of the x is the year after 1980. It shows that for the year 2020, the value of the x is
$\begin{align}
& x=2020-1980 \\
& =40
\end{align}$
Consider the obtained function from part$\left( \text{a} \right)$:
$M\left( x \right)=8x+470$
Substitute x as 40 in the above equation:
$\begin{align}
& M\left( 40 \right)=8x+470 \\
& =8\left( 40 \right)+470 \\
& =790
\end{align}$
Thus, the number of bachelor’s degree that will be awarded to men in 2020 is 790 thousand.
