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 1790 4.5 1910 26 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: Identify given values

$x=210$, $\hat{y}=5.56821(1.01264)^x$

Step2: Substitute $x$ into equation

$\hat{y}=5.56821(1.01264)^{210}$

Step3: Calculate exponent first

$1.01264^{210}\approx22.0537$

Step4: Multiply to find $\hat{y}$

$\hat{y}=5.56821\times22.0537\approx122.8$

Answer:

122.8 people per square mile