Q46. - Algebra 2

Question

For Exercises 45-47, use the graphic that shows 2000 state populations. 

46. Graph both equations for the years 2000 to 2020. Estimate when the populations of both the states will be equal.

Step-by-Step Solution

Answer

The equation that represent population of Florida is $y=304000x+15982000$ and population of New York is $y=98600x+18976000$. Graph of the equations is provided below.

The population of both the states will be equal in 2015 and population will be 20,410,000.

Step-1 – Interpret the data

According to the question, population y of states x years after 2000 is to be computed.

It is assumed that states continue to gain the same number of residents evey year.

Step-2 – Define the variables

Consider two variables x and y.

Denote the population after 2000 by x and total population by y.

Step-3 – Build the equations

The population of Florida in 2000 is 15,982,000 and average annual gain is 304,000.

Therefore, the equation that represent population of Florida is provided below.

 $y=304000x+15982000$

The population of New York in 2000 is 18,976,000 and average annual gain is 98,600.

Therefore, the equation that represent population of Florida is provided below.

$y=98600x+18976000$

 

Thus, the equation that represent population of Florida is $y=304000x+15982000$ and population of New York is $y=98600x+18976000$.

Step-4 – Graph the equations

Plot the equations $y=304000x+15982000$ and $y=98600x+18976000$ on the Cartesian Plane from 2000 to 2020, that means x lies between 0 and 20.

The red line denote the equation $y=304000x+15982000$ and purple line denote the equation $y=98600x+18976000$.

Step-5 – Interpret the graph

The graphs intersect at the point $\left(14.576,20410000\right)$.

This means the population of both the states will be equal in 2015 and population will be 20,410,000.