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Math Help - Log Question

  1. #1
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    Log Question

    Hello people, i got this log question and it took me ages and i still can not figure it out, can anyone explain this to me?

    Q: The population of Cda is 30 m and is growing at an annual rate of 1.4%
    The population of Ger is 80 m and is decreasing at an annual rate of 1.7%
    In how how many years will the population of Cda be equal to the population of Ger?
    (use log to solve the resulting equation and to 2 decimal places)

    The answer is 31.59 yrs but i have no idea how to do it, any ideas?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by rudyzhou2 View Post
    Hello people, i got this log question and it took me ages and i still can not figure it out, can anyone explain this to me?

    Q: The population of Cda is 30 m and is growing at an annual rate of 1.4%
    The population of Ger is 80 m and is decreasing at an annual rate of 1.7%
    In how how many years will the population of Cda be equal to the population of Ger?
    (use log to solve the resulting equation and to 2 decimal places)

    The answer is 31.59 yrs but i have no idea how to do it, any ideas?
    use the exponential growth/decay formulas.

    For Cda: P_1(t) = 30e^{0.014t}

    where P_1(t) is the population (in millions) at time t since the population was 30mill

    For Ger: P_2 = 80e^{-0.017t}

    where P_2(t) is the population (in millions) at time t since the population was 80mill

    we want to solve P_1(t) = P_2(t) for t

    do you think you can continue?
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  3. #3
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    oh god i see now it's natural -0.017, i did it for 0.017 lol thank you very much!
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