Question

The population of two different villages is modeled by the equations shown

Answer 1

Answer:

Year = 1995 and population = 315

Year = 2015 and population = 715

Step-by-step explanation:

It is given that the population of two different villages is modeled by the given equations:

$y=x^2-30x+540$

$y=20x+15$

The population of both villages are same after x years after 1980 if

$x^2-30x+540=20x+15$

$x^2-30x+540-20x-15=0$

$x^2-50x+525=0$

Splitting the middle term, we get

$x^2-15x-35x+525=0$

$x(x-15)-35(x-15)=0$

$(x-15)(x-35)=0$

$x=15,35$

It means, after 15 or 35 years, the population will same.

For x=15, years is $1980+15=1995$ and population is  

$y=20(15)+15=315$

For x=35, years is $1980+35=2015$ and population is  

$y=20(35)+15=715$.

Therefore, population are equation in Year = 1995 and population = 315 or Year = 2015 and population = 715.