Answer
a) $\hspace{0.1cm} y=14792.1t-490415.6$
b) $\hspace{0.1cm} y=1210675.9$
c) Not valid in reality
Work Step by Step
a) Since the change in immigration is linear, we can write the linear equation as:
$y=mt+c$ where,
$y$ is the number of immigrants,
$t$ is the number of years after 1900,
$m$ is the slope and $c$ the $y$-intercept.
$m=\frac{y_2-y_1}{t_2-t_1}=\frac{1107126-249187}{108-50}=14792.051$
substituting $(t,y)=(50,249187)
$ and $m=14792.051$ in the linear function we get,
$c=y-mt=249187-(14792.051\times50)=-490415.586$
Therefore the linear function is $y=14792.1 t-490415.6$.
b) The number of immigrants to US in the year 2015, i.e. $t=2015-1900=115$ is,
$y=(14792.1\times115)-490415.6=1210675.9$ ( Substituting in the equation obtained in part (a))
c) The $y$-intercept is $c=-490415.6$ which implies that in the year 1900, the number of immigrants are $-490415.6$ which is not possible. So our equation is not valid because the change in immigration is not linear in real world, but we have assumed it is linear in part (a).
