Answer
$a.\quad R(t)=-0.02t+19.81$
$b.\quad 19.01$ seconds
Work Step by Step
$ a.\quad$
We are given two points on the graph of R(t),
(3,19.75) ... for the year 1980+3=1983
(31,19.19)... for the year 1980+31=2011
The slope of the line is $m=\displaystyle \frac{19.19-19.75}{31-3}=\frac{-0.56}{28}=-0.02$
The point slope line equation is
$y-19.75=-0.02(t-3)$
$y=-0.02t+0.06+19.75$
$R(t)=-0.02t+19.81$
$ b.\quad$
In 2020, $t=40$
$R(40)=-0.02(40)+19.81=19.01$ seconds
