Answer
a) See below
b) The linear function that models the life expectancy is $E\left( x \right)=0.215x+65.7$.
c) The life expectancy of American men born in $2020$ is $78.6\text{yrs}$.
Work Step by Step
(b)
The slope of the line passing through the given points $\left( 20,70 \right)$ and $\left( 40,74.3 \right)$ is:
$\begin{align}
& m=\frac{74.3-70}{40-20} \\
& =0.215
\end{align}$
The equation of the line passing through these points can be given by
$\begin{align}
& y-70=0.215\left( x-20 \right) \\
& y=0.215x+65.7 \\
\end{align}$
Here, $y$ is a function of $x$, i.e. $y=E\left( x \right)$
Therefore, the linear function that models the life expectancy is $E\left( x \right)=0.215x+65.7$.
(c)
Consider the linear function,
$E\left( x \right)=0.215x+65.7$
Where, $x$ is the number of years after $1960$ and $E\left( x \right)$ is the life expectancy of American males.
In $2020$ ,
$\begin{align}
& x=2020-1960 \\
& =60
\end{align}$
Substitute the value of $x$ in the given equation,
$\begin{align}
& E\left( x \right)=0.215\cdot 60+65.7 \\
& =78.6
\end{align}$
Therefore, the life expectancy of American men born in $2020$ is $78.6\text{yrs}$.
