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Math Help - logs help urgent

  1. #1
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    logs help urgent

    Hey.

    Could someone help me on this question because i am stuck. Am i doing the wrong thing?

    Write down the function which could be used to estimatethe GDP of a particular country in t years time, when the current GDP equals A units, and which grows at r% per annum, where growth is continuous.

    Use this function, estimate the annual average percentage rate of growth r, when GDP of a country grows from 250 units to 420 units in 8 years.

    GDP = Ae^8

    lnGDP = lnA + lne^8

    = 170 + 2980

    = 3150

    This doesn't look right could someone tell me what im doing wrong?

    THanks
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  2. #2
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    Quote Originally Posted by Stem01 View Post
    Hey.

    Could someone help me on this question because i am stuck. Am i doing the wrong thing?

    Write down the function which could be used to estimatethe GDP of a particular country in t years time, when the current GDP equals A units, and which grows at r% per annum, where growth is continuous.

    Use this function, estimate the annual average percentage rate of growth r, when GDP of a country grows from 250 units to 420 units in 8 years.

    GDP = Ae^8

    lnGDP = lnA + lne^8

    = 170 + 2980

    = 3150

    This doesn't look right could someone tell me what im doing wrong?

    THanks
    1. I would use:

    GDP(t)=A \cdot \left(1+\dfrac r{100}\right)^t

    2. You'll get an approximate value if you use:

    GDP(t)=A \cdot e^{\left(\frac r{100}\right) \cdot t}

    3. With your question you get:

    420=250 \cdot e^{\left(\frac r{100}\right) \cdot 8}

    \dfrac{420}{250}= e^{\left(\frac r{100}\right) \cdot 8}

    \ln(420)-\ln(250)= 8 \cdot \frac r{100}

    \dfrac{100(\ln(420)-\ln(250))}8=  r

    \boxed{r\approx 6.485\ \%}
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  3. #3
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    Thanks soo much for your help.

    Aothe average percentage growth rate = 6.5%
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