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    Hi, I was just wondering if I could get some help with a maths question I'm struggling with.
    The question is as follows (Cambridge Advanced Mathematics, Core 3, page 77, exercise 5B, question 9b);
    "An epidemic is spreading exponentially through a community so that the total number of people who have been admitted to hospital in the first t weeks (including those who have subsequently been discharged) is modelled by the equation y=5(e^0.3t)"
    (Where 'e' is the constant 2.718 etc...)

    I am fine with part a).

    "a) At what rate are new patients being admitted;
    i) after 5 weeks
    ii) after 200 people have already been admitted"

    However, I am struggling with part b) for which I have no clue what to do

    "b) Patients remain in the hospital for two weeks and are then discharged. Find an expression for the number of patients in hospital after t weeks (for t [is more than or equal to] 2), and show that this number also increases exponentially."

    So there you have it... I feel like Homer Simpson.

    Please could you explain the question in great detail, and I mean GREAT detail, any equations or anything you find, please explain where you found them (but I'm drawing the line under deriving any formulas!).

    Thanks a lot

    And also, I'm putting the answer below- so if you don't want to find it out, don't keep reading.

    Answer: 2.26(e^0.3t)

    The rate at which patients are entering:
    \frac{dy}{dt} = 1.5e^{0.3t}

    The patients leave after two weeks, so the number leaving is modelled by:

    Adding together to take account of both effects:
    \frac{dy}{dt} = 1.5e^{0.3t} - 1.5e^{0.3(t-2)}
     \frac{dy}{dt} = 1.5e^{0.3t}(1 - e^{-0.6})
     \frac{dy}{dt} = 1.5e^{0.3t}(0.451...)
     \frac{dy}{dt} = 0.67678...e^{0.3t}

    Integrate to get number of patients:
    y = 2.2559...e^{0.3t}
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