Question

the us population density (people per square mile) for the past several decades is given in the table below.

year	people per square mile	year	people per square mile
1800	6.1	1920	29.9
1810	4.3	1930	34.7
1820	5.5	1940	37.2
1830	7.4	1950	42.6
1840	9.8	1960	50.6
1850	7.9	1970	57.5
1860	10.6	1980	64
1870	10.9	1990	70.3
1880	14.2	2000	80
1890	17.8	2010	87.4
1900	21.5	2020	93.8

an exponential regression on the data results in the equation $y = 5.56821(1.01264)^x$, where $x$ is the number of years since 1790 and $y$ is the number of people per square mile.

use the regression equation to extrapolate approximately how many people per square mile there will be in the year 2100 which is 310 years since 1790.

people per square mile (round your answer to the nearest tenth)

Explanation:

Step1: Substitute x=310 into equation

Substitute $x=310$ into $y = 5.56821(1.01264)^x$:
$y = 5.56821(1.01264)^{310}$

Step2: Calculate exponent term

First compute $(1.01264)^{310}$. Using a calculator:
$(1.01264)^{310} \approx 48.623$

Step3: Multiply by initial coefficient

Multiply the result by 5.56821:
$y \approx 5.56821 \times 48.623$
$y \approx 270.7$

Answer:

270.7 people per square mile