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Math Help - Sequences and Series

  1. #1
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    Sequences and Series

    The question is posted below and I have attached my solution, which is close to the values in the answer section, but only when I round it.

    Each year for the past five years the population of a certain counry has increased at a steady rate of 2.7% per annum. The present population is 15.2 million.
    a) What was the population one year ago?
    b) What was the population five years ago?

    My solution:
    U6 (6th term)=15.2 million
    common ratio=1.027
    U1 = first term

    U6 = U1(1.027)^5
    15.2 million = U1(1.027)^5

    Therefore, b) U1=13.3 million
    and a) U5 (fifth term) = U1(1.027)^4
    = 13.3(1.027)^4
    = 14.8 million

    Now, the answer in the book is: a) 14 793 187 b) 13 271 941
    even if I don't round my values, they still aren't the same as the book's. Did I do this question right?
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  2. #2
    Senior Member AllanCuz's Avatar
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    Quote Originally Posted by bhuang View Post
    The question is posted below and I have attached my solution, which is close to the values in the answer section, but only when I round it.

    Each year for the past five years the population of a certain counry has increased at a steady rate of 2.7% per annum. The present population is 15.2 million.
    a) What was the population one year ago?
    b) What was the population five years ago?

    My solution:
    U6 (6th term)=15.2 million
    common ratio=1.027
    U1 = first term

    U6 = U1(1.027)^5
    15.2 million = U1(1.027)^5

    Therefore, b) U1=13.3 million
    and a) U5 (fifth term) = U1(1.027)^4
    = 13.3(1.027)^4
    = 14.8 million

    Now, the answer in the book is: a) 14 793 187 b) 13 271 941
    even if I don't round my values, they still aren't the same as the book's. Did I do this question right?
    This type of question is modeled by

    P=Pie^{rt}

    Where r = rate, t = time, Pi= Initial Population. Let us define t in years. Let us find the intial Population

    15.2 = Pie^{.027(5)}

    Pi=13.28

    Now let us find the population at year 4

    P=13.28e^{(.027)(4)}=14.8

    Your book asks for the answers in reverse order. Oh and this is not a sequence or series question, it is an exponential growth question (for future reference)! You got the same answers as me, yes your answers are correct.
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