Respuesta :
Answer:
16 years.
Step-by-step explanation:
Please consider the complete question.
Assume that the suburb has a population of 686,000 and is growing at a rate of 4000 per year. Assume that the city has a population of 942,000 and is declining at a rate of 12000 per year. In how many years will the populations of the suburb and the city be equal?
Let x represent number of years.
Growth function would be [tex]G(x)=4000x+686,000[/tex] and decline function would be [tex]D(x)=942,000-12,000x[/tex].
To find the time when both populations will be equal, we will equate both functions as:
[tex]4000x+686,000=942,000-12,000x[/tex]
[tex]4000x+12,000x+686,000=942,000[/tex]
[tex]16,000x+686,000=942,000[/tex]
[tex]16,000x=942,000-686,000[/tex]
[tex]16,000x=256,000[/tex]
[tex]\frac{16,000x}{16,000}=\frac{256,000}{16,000}[/tex]
[tex]x=16[/tex]
Therefore, in 16 years the populations of the suburb and the city will be equal.
