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Thread: Exponential growth and decay question

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    Exponential growth and decay question

    The population of a city is P(t) at any one time. The rate of decline in population is proportional to the population P(t), that is, dP(t)/dt = -KP(t).
    What will the percentage rate of decline in population be after 10 years?

    (k = ln(0.9)/-4
    Last edited by jadg; 26 May 2018 at 6:49 PM.

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    Re: Exponential growth and decay question

    The picture is not there.

    Are you given the initial population of the city at ?
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    Re: Exponential growth and decay question

    Sorry it wont upload
    that is the whole first bit of the question, it then asks
    a) Show that P(t)=P(t(subscript 0))e^-kt is a solution of the differential equation dP(t)/dt = -KP(t)
    and
    b) What percentage decline will there be after 10 years, given a 10% decline in 4 years? (answer = 23%)
    and then c) as above, no initial value

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    Re: Exponential growth and decay question

    Assuming you have done a) and b), you would have



    Then substitute and you will get the population after 10 years as a percentage of the original population .
    Last edited by fan96; 27 May 2018 at 2:46 PM.
    HSC 2018: [English Adv.] • [Maths Ext. 1] • [Maths Ext. 2] • [Chemistry] • [Software Design]

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