In 2002, the population of a certain country per square mile of land area was 84

Question

In 2002, the population of a certain country per square mile of land area was 84. In? 2000, the person per square mile population was 82.8. Assume the relationship between years and persons per square mile is a linear relationship.
a. Write an? equation, in? slope-intercept form, describing the relationship between year and persons per square mile. Use ordered pairs of the form left parenthesis x comma y right parenthesis?, where x is the number of years past 2000 and y is persons per square mile.
b.Use this equation to predict the person per square mile population in 2030.

a. What is the equation describing the linear? relationship?
y= ?

b. Use the equation from part? (a) to determine the person per square mile population in 2030.
? persons per square mile

Explanation / Answer

a. Let the equation describing the linear relationship between the population of a certain country per square mile of land area(y) and the number of years since 2000 (x) be y = mx +c, where m and c are arbitrary real numbers.

In 2000, x = 0 and y = 82.8, so, on substituting x = 0 and y = 82.8 in the above equation, we get c = 82.8. Then, the above equation changes to y = mx+82.8. Further, in 2002, x = 2 and y = 84 so that 84 = 2x +62.8 or, 2x = 84-82.8 = 1.2 . Therefore, x = 1.2/2 = 0.6. Thus, y = 0.6x+82.8.

b. In 2030, we have x = 2030-2000= 30. On substituting x = 30 in the above equation, we get y = 0.6*30 +82.8 = 18+82.8 = 100.8. Hence, the population of the country per square mile of land area, in 2030, would be 100.8 persons.

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