Answer
(a.) $1390$ billionaires, Overestimate by $164$ billionaires.
(b.) The year is $2018$.
Work Step by Step
The given function is
$f(x)=2x^2+140$
(a.) The value of $x$ in $2012−1987=25$
Plug $x=25$ into the function.
$f(25)=2(25)^2+140$
$f(25)=2(625)+140$
$f(25)=1250+140$
$f(25)=1390$
From the graph the number of billionaires in $2012$ is $1226$.
The difference is $1390−1226=164$.
Hence, the function overestimates by $164$ billionaires.
(b.) The given value of $f(x)$ is $2062$.
Plug $f(x)=2062$
$2062=2x^2+140$
Subtract $140$ from both sides.
$2062−140=2x^2+140−140$
Simplify.
$1922=2x^2$
Divide both sides by $2$.
$\frac{1922}{2}=\frac{2x^2}{2}$
Simplify.
$961=x^2$
Take square root on both sides.
$\sqrt{961}=\sqrt{x^2}$
Simplify.
$31=x$
The year is $1987+31=2018$.
