precalculus

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the population of a country is 65 millions if it grows exponentially in a rate of 1.5% annual

1.-calculate the estimate population in 12 years


2.-when the population increases 4 times



could somebody please explain me this kind of problems where you need to use the log and please tell me the answers

  • precalculus -

    1. .015*65*12+65=76.7 million
    2. 4*65=260 million

  • precalculus -

    1. Multiply 65 million by (1.015)^12

    (1.015^12 = 1.1956)

    2. Multiply 65 million by 4.

    You don't need to use log for the second one.

    You can to 1. with a log table or with a hand calculator (as I did).

    If you use logs:
    Log (answer) = log (65 million) + 12 log 1.015
    Then take the antilog

    You will learn more if you do the calculations yourself than if I gave you the numerical answers.

  • precalculus -

    Let
    P = population in millions
    t = time in years

    Population growth is continuous. For continuous compounding use the formula:

    P = 65*e^(.015t)

    For the population in 12 years we have:

    P = 65*e^(.015*12) = 65*e^(.18)
    P = 77.8 million

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