Answer
(a.) Births per day $=384,000$.
Deaths per day $=156,000$.
(b.) $83$ million.
(c.) $4$ years.
Work Step by Step
Let the number of births $=A$.
and the number of deaths $=B$.
From the question we have
$\Rightarrow A=3B-84$ thousand...... (1)
(a.) Population increase in a signle day $=A-B$. thousand.
From the question we have $A-B=228$ thousand.....(2)
Plug the value of $A$ from equation (1) to equation (2).
$\Rightarrow (3B-84)-B=228$
Simplify.
$\Rightarrow 3B-84-B=228$
$\Rightarrow 2B-84=228$
Add $84$ to both sides.
$\Rightarrow 2B-84+84=228+84$
Simplify.
$\Rightarrow 2B= 312$
Divide both sides by $2$.
$\Rightarrow \frac{2B}{2}= \frac{312}{2}$
Simplify.
$\Rightarrow B= 156$
Plug the value of $B$ into equation (1).
$\Rightarrow A=3(156)-84$
Simplify.
$\Rightarrow A=468-84$
$\Rightarrow A=384$
Hence, the number of births per day $=384,000$.
The number of deaths per day $=156,000$.
(b.) Population increase in a single day $=228$ thousand.
Multiply the population increase per day by $365$.
$=228\times 365$
$=83220$ thousands.
$=83,220,000$
Rounded to the nearest million
$=83$ million.
(c.) From the part (b.) per year increase $=83$ million.
Let the number years for the population increases by an amount greater than the entire U.S. population $320$ million $=t$.
$t=\frac{320}{83}$
Simplify.
$t=3.85542$
Rounded value.
$t=4$ years.
