Maths Exponential modelling Edexcel question help!

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WingsDan
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#1
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The number of people infected with a disease is modelled by a formula
N=300-100e^-0.5
Where N is the number of people infected with the disease and t is the time in years after detection
b)what is the long term prediction of how this disease will spread?
c) sketch the graph of N against t for t>0
The answer at the back of the book says that the disease will infect up to 300 people(for b)
I don't understand how it wll be 300 people? The graph drawn for question c shows that it starts at 300..but doesn't it start at 200 because if you subtitute 0 in for t in the formula to get the number of people infected at the beginning you'd get 200?
please help me for both questions
Many thanks
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ghostwalker
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(Original post by WingsDan)
The number of people infected with a disease is modelled by a formula
N=300-100e^-0.5
Where N is the number of people infected with the disease and t is the time in years after detection
b)what is the long term prediction of how this disease will spread?
c) sketch the graph of N against t for t>0
The answer at the back of the book says that the disease will infect up to 300 people(for b)
I don't understand how it wll be 300 people? The graph drawn for question c shows that it starts at 300..but doesn't it start at 200 because if you subtitute 0 in for t in the formula to get the number of people infected at the beginning you'd get 200?
please help me for both questions
Many thanks
If the graph starts at 300, then, yes, it's incorrect. It should start at 200 and go up from there. Does this clear up your problem with (b) as well?
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WingsDan
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(Original post by ghostwalker)
If the graph starts at 300, then, yes, it's incorrect. It should start at 200 and go up from there. Does this clear up your problem with (b) as well?
Oh, but the exponential function has a negative power so wouldn't it go down and not up??? Is there like a rule for the positive/negative powers
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ghostwalker
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(Original post by WingsDan)
Oh, but the exponential function has a negative power so wouldn't it go down and not up??? Is there like a rule for the positive/negative powers
Yes, the exponential function does have a negative power, and as t increases it will decrease. But, it's being subtracted, so as the exponential decreases the overall function increases.
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