Population in 2014=23.2 million
Population in 2018=26.8 million
Population in 2024= ?
The population increase is linear, therefore:
[tex]p(t)=m*t+b[/tex]
Where t, time since 2005 and p is the population.
We know two points:
P1= (t, p) = (2014, 23.2)
P2=(t , p)=(2018, 26.8)
But the time is since 2005, then:
2014-2005=9
2018-2005= 13
The points are:
P1= (t1, p1) = (9, 23.2)
P2=(t2 , p2)=(13, 26.8)
The slope is going to be:
[tex]m=\frac{p_2-p_1}{t_2-t_1}=\frac{26.8-23.2}{13-9}=\frac{9}{10}=0.9[/tex]
Replacing any point in the equation to find b:
[tex]\begin{gathered} p(t)=0.9*t+b \\ 23.2=0.9*9+b \\ b=23.2-8.1=15.1 \end{gathered}[/tex]
The equation is:
[tex]p(t)=0.9*t+15.1[/tex]
Where 15.1 millions is the population in 2005.
Finally, the population in 2024 will be:
[tex]\begin{gathered} 2024-2005=19 \\ p=0.9*19+15.1=32.2 \end{gathered}[/tex]
Answer: The population of Nevada in 2024 is: 32.2 millions.
