Question

Enter the minimum number of years it will take the population of North Dakota to equal the population of South Dakota given the current rates of growth. Round your answer to the nearest tenth of a year?

The population of North Dakota in 2012 is 0.70 million people. North Dakota has a yearly population growth of 0.028 million people. The population of South Dakota in 2012 is 0.83 million people. South Dakota has a yearly population growth of 0.0195 million people.

Answer 1

15.3 years

Explanation:

First off, we'll assume that the rates of population growth won't change.

The population of North Dakota in Year 0 is 700,000 people and is growing by 28,000 people per year. We can say then that the population of North Dakota in any given year is:

`700,000+28,000Y=P` where `Y` stands for years and `P` for population.

We can do the same with South Dakota:

`830,000+19,500Y=P`

We're interested in what `Y` the populations of North and South Dakota are equal:

`700,000+28,000Y=830,000+19,500Y`

`700,000+28,000Ycolor(red)(-700,000-19,500Y)=830,000+19,500Ycolor(red)(-700,000-19,500Y)`

`8500Y=130,000=>Y~~15.3`

And just for fun, that population will be roughly 1,128,235 people.