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# Help With Exponentials and Decay watch

1. 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

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.

2. The rate at which patients are entering:

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

Adding together to take account of both effects:

Integrate to get number of patients:

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Updated: January 28, 2015
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