Answer
(a.) $940$ billionaires, Underestimate by $6$ billionaires.
(b.) The year is $2017$.
Work Step by Step
The given function is
$f(x)=2x^2+140$
(a.) The value of $x$ is $2007-1987=20$
Plug $x=20$ into the function.
$f(20)=2(20)^2+140$
$f(20)=2(400)+140$
$f(20)=800+140$
$f(20)=940$
From the graph the number of billionaires in 2007 is $946$.
The difference is $946-940 = 6$.
Hence, the function underestimates by $6$ billionaires.
(b.) The given value of $f(x)$ is $1940$.
Plug $f(x)=1940$
$1940=2x^2+140$
Subtract $140$ from both sides.
$1940-140=2x^2+140-140$
Simplify.
$1800=2x^2$
Divide both sides by $2$.
$\frac{1800}{2}=\frac{2x^2}{2}$
Simplify.
$900=x^2$
Take square root on both sides.
$\sqrt {900}=\sqrt {x^2}$
Simplify.
$30=x$
The year is $1987+30 = 2017$.
