Answer
a. 157.852 million is the U.S. population on July 1 1952.
b. 1949 is the year that the U.S. population reached 150 million.
Work Step by Step
Given:
$y=2.8370x + 140.83$
$year=1952$
Solve for x:
$x=year - 1946$
$x=1952 - 1946$
$x=6$
Solve for y and substitute the x value
$y=2.8370x + 140.83$
$y=2.8370(6) + 140.83$
$y=2.8370(6) + 140.83$
$y=157.852$ millions
a. 157.852 million is the U.S. population on July 1 1952
to solve item b, substitute 150 to y
$y=2.8370x + 140.83$
$150=2.8370x + 140.83$
move 140.83 to the left side
$150-140.83=2.8370x$
$9.17=2.8370x$
divide both sides by 2.8370
$\frac{9.17}{2.8370}=\frac{2.8370x}{2.8370}$
$3.23=x$
$3=year - 1946$
$3+1946=year$
$year=1949$
b. 1949 is the year that the U.S. population reached 150 million.
