A population doubles every 34 years. Assuming exponential growth find the following?

(a) The annual growth rate is __________% per year

(b) The continuous growth rate is ________% per year

3 Answers

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  • david
    Lv 7
    3 weeks ago

    A(t) = Ao X 2^(t/34) ..... assume the initial amount is 1 then A(34) = 2

    2 = 1 X 2^34/34 = 2 ... see, it works

    A(1) = 1 X 2^(1/34) = 1.02059591 = an increase of 0.02059591 in one year .. or 2.059591% per year

    ====================================

    A(t) = (Ao)e^rt

    2 = (1)e^(r*34)

    34r = ln2

    r = 0.020386681

    or as a percent .. r = 2.0386681 % continuous

  • Alan
    Lv 7
    3 weeks ago

    logic says this is a valid equation.

    A(t) = A_o *(2)^(t/34)

    (a) annual rate (I think)

    need form

    A(t) = A_o*( 1+ a.aa)^t

    A(t) =A_o* ((2)^(1/34))^t

    A(t) = A_o*(1.02059591)^t

    A(t) = A_o(1 + 0.02059591)^t

    Annual Rate = 2.0589591 %

    so for continuous rate (I'm sure is ) :

    so to get (b) convert to

    form A(t) =A_o*e^(kt)

    A(t) = A_o*e^(ln(2)t/34)

    so k = ln(2)/34 = 0.020386682

    Continuous Rate = 2.038666 %

  • 3 weeks ago

    a) %growth = 70/DoublingTime = 2%

    b)same as a i think

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