SOLUTION: In 1982 the population density of a country was 64 people per square mile, and in 2002 it was 82 people per square mile. Use a linear function to estimate when the population densi

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Question 1196962: In 1982 the population density of a country was 64 people per square mile, and in 2002 it was 82 people per square mile. Use a linear function to estimate when the population density reached 89 people per square mile
Answer by ikleyn(52780) About Me  (Show Source):
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In 1982 the population density of a country was 64 people per square mile,
and in 2002 it was 82 people per square mile.
Use a linear function to estimate when the population density reached 89 people per square mile
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In 20 years from 1982 to 2002, the average rate of increasing population density was

    r = %2882-64%29%2F20 = 18%2F20 = 0.9 of a person per square mile per year.


So, assuming that this rate remains constant, we write this linear equation for the future density

    D = 82 + r*(t-2002).


To find a year when the density will reach 89 p/sq.mile, we write equation

    82 + 0.9*(t-2002) = 89,


and we find

    t-2002 = %2889-82%29%2F0.9 = 7%2F0.9 = 7.777...


It tells us that the density 89 p/sq.mile will be reached somewhen in the year 2009 or 2010
depending on from which time moment in the year 2002 we started out our time counter (chronometer).    ANSWER

Solved.