Algebra sequences

Year 2003 2004 2005 2006

Populatation 22.12 22.49 22.86 23.41

A. divide the population for each year by the population in the preceeding year. Round to the two decimal places and show the Texas population increase that is approximately geometric.

1.01
B. Write the general term of the geometric sequence modeling texas population in millions n years in 2002.

an= 22.12 (1.01)n-1

C. Use your model from part (b) to project texas's population in millions for the year 2010. round to two decimal places.

approximately 26.4

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  1. A. The average is closer to a factor of 1.02 increase each year. The ratios for each year are 1.017, 1.017 and 1.024

    B. 2002 is one year before 2003, so
    22.12/1.02 = 21.69 (million)
    is the population in 2002

    It isn't clear if they are asking for the general term or the population in 2002.

    A model equation for year 2003 + n would be 22.12*1.02^n
    Use n = -1 for 2002

    C. 2010 is 2003 + 7
    22.12*(1.02)^7 = 25.4 million

    I don't see how you got 26.4 using 1.01 as the annual increase factor

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  2. r for 2004 : 22.49/22.12 = 1.0167 = 1.02
    r for 2005 : 22.86/22.49 = 1.01645 = 1.02
    r for 2006 : 23.41/22.86 = 1.0241 = 1.02

    so rounded to 2 decimals like it asked for the rate appears to be 2% or the r = 1.02

    B) population = 22.12(1.02)^(n-2003) where n is the year.
    check: for the year 2006 ....
    pop = 22.12(1.02)^(2006-2003) = 22.12(1.02)^3 = 23.47 (close enough?)

    so in 2002 they had 22.12(1.02)^-1 = 21.69

    C) for 2010 : pop = 22.12(1.02)^7 = 25.41

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