Someone me 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. 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.

It will take 10.3 years for the population of North Dakota to equal the population of South Dakota.

Solution:
First, we calculate for the growth rate from the given yearly population growth of 
     North Dakota: 0.028/0.70 = 0.040 or 4.0%
     South Dakota: 0.0195/0.83 = 0.023 or 2.3%

The population of North Dakota after t years is 
     0.70(1+0.04)^t 
while the population of South Dakota after t years is
     0.83(1+0.023)^t

We equate the above expressions to find the number of years t it will take the two populations to be equal: 
     0.70(1+0.04)^t = 0.83(1+0.023)^t 
     0.70(1.04)^t = 0.83(1.023)^t 
     (1.04)^t / (1.023)^t = 0.83/0.70

After taking the log of both sides of our equation, number of years t is
     t = log (0.83/0.70) / log (1.04/1.023) = 10.3 years

The slope of the function is 0.5.