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Math Help - logistic growth

  1. #1
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    logistic growth

    i really dont no what the hell to do for this question

    can some1 guide me tru this 1

    The logistic growth function
    f(t) = (83,000 ) / 1 + 2074e^-1.6t

    models the number of people who have become ill with a
    particular infection t weeks after its initial outbreak in a particular community. How many people were ill after
    8 weeks?
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  2. #2
    MHF Contributor Unknown008's Avatar
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    f(t) = \dfrac{83000}{1+2074e^{-1.6t}}

    Put t = 8
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  3. #3
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    therefore
    <br />
f(t) = \dfrac{83000}{1+2074e^{-1.6(8)}}<br /> <br /> <br /> <br />
f(t) = \dfrac{83000}{1+2074e^{-12.8}}<br />

    AM I GOING CORRECT
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  4. #4
    MHF Contributor Unknown008's Avatar
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    Yes, and the tabs are [tex] and not [code]
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  5. #5
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    is this correct

    <br />
f(t) = \dfrac{83000}{(1+2074)(2.76)}<br /> <br />
f(t) = \dfrac{83000}{5727}<br /> <br />
    f(t) = 14.49<br />
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  6. #6
    MHF Contributor Unknown008's Avatar
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    From here... no.

    e^{-12.8}  = 2.76 \times 10^{-6}

    This multiplied by 2074 will give a very small number, less than 1.
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  7. #7
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    From here... no.

    e^{-12.8} = 2.76 \times 10^{-6}

    This multiplied by 2074 will give a very small number, less than 1.
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  8. #8
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    <br /> <br />
f(t) = \dfrac{83000}{1+2074(0.0000276)}<br /> <br />
f(t) = \dfrac{83000}{1+0.0572}<br /> <br />
f(t) = \dfrac{83000}{1.06}<br />

    is this it
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  9. #9
    MHF Contributor Unknown008's Avatar
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    Quite.

    You missed a zero.

    f(t) = \dfrac{83000}{1+2074(0.00000276)}

    f(t) = \dfrac{83000}{1+0.00572}
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  10. #10
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    <br />
    f(t) = \dfrac{83000}{1.00572}<br />
[br]<br />
   f(t) = 82527.9<br />
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  11. #11
    MHF Contributor Unknown008's Avatar
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    This should be okay

    When I input this in my calculator, I get:

    f(t) = \dfrac{83000}{1+2074e^{-1.6(8)}} = 82527.46077...

    It's fairly close since you too the approximation of the exponential.
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  12. #12
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    thanks again for all the help u have given me
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