Question

Suppose the U.S bureau projects the population of Texas to be 23.2 million in 2014 and 26.8 million in 2018. Assuming the population growth is linear , use (t) years since 2005 and (p) the population of Texas in millions. What is the population of Nevada in 2024?

Answer 1

Population in 2014=23.2 million

Population in 2018=26.8 million

Population in 2024= ?

The population increase is linear, therefore:

`p(t)=m*t+b`

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:

`m=(p_2-p_1)/(t_2-t_1)=(26.8-23.2)/(13-9)=(9)/(10)=0.9`

Replacing any point in the equation to find b:

`\begin{gathered} p(t)=0.9*t+b \\ 23.2=0.9*9+b \\ b=23.2-8.1=15.1 \end{gathered}`

The equation is:

`p(t)=0.9*t+15.1`

Where 15.1 millions is the population in 2005.

Finally, the population in 2024 will be:

`\begin{gathered} 2024-2005=19 \\ p=0.9*19+15.1=32.2 \end{gathered}`

Answer: The population of Nevada in 2024 is: 32.2 millions.