A linear model estimates the population of a city from 1991 to 2015 . The model estimates the population was

Question

A linear model estimates the population of a city from 1991 to 2015 . The model estimates the population was 57 thousand in 1991 , 224 thousand in 2011 , and x thousand in 2015 . To the nearest whole number, what is the value of x ?

Accepted Answer

The correct answer is 257 . It&rsquo;s given that a linear model estimates the population of a city from 1991 to 2015 . Since the population can be estimated using a linear model, it follows that there is a constant rate of change for the model. It&rsquo;s also given that the model estimates the population was 57 thousand in 1991 , 224 thousand in 2011 , and x thousand in 2015 . The change in the population between 2011 and 1991 is 224 - 57 , or 167 , thousand. The change in the number of years between 2011 and 1991 is 2011 - 1991 , or 20 , years. Dividing 167 by 20 gives 167 / 20 , or 8.35 , thousand per year. Thus, the change in population per year from 1991 to 2015 estimated by the model is 8.35 thousand. The change in the number of years between 2015 and 2011 is 2015 - 2011 , or 4 , years. Multiplying the change in population per year by the change in number of years yields the increase in population from 2011 to 2015 estimated by the model: 8.35 4 , or 33.4 , thousand. Adding the change in population from 2011 to 2015 estimated by the model to the estimated population in 2011 yields the estimated population in 2015 . Thus, the estimated population in 2015 is 33.4 + 224 , or 257.4 , thousand. Therefore to the nearest whole number, the value of x is 257 .

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