Gas Guzzlers

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Gas Guzzlers
Are there more cars with larger engines on the
roads today?
Source www.dft.gov.uk
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What type of function might provide a good model?
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Finding an exponential model
N N0ekt
ln N ln (N0ekt)
Taking logs base e
ln N ln N0 ln ekt
Using the laws of logs
ln N ln N0 kt ln e
ln N ln N0 kt
y c mx
Compare with
Drawing a graph of ln N against t should give a
straight line.
If so, its gradient will give k and its intercept
will give ln N0.
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Cars registered with engine size 2 litres or more
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(No Transcript)
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k gradient 0.0704
ln N0 intercept 7.318
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ln N0 7.318
From the graph
N0 e7.318
1507
Calculate N0
N 1507e0.0704t
Exponential model
How good is this model?
N 1507e0.0704 6
2299
eg in 2000 i.e. when t 6
error
error
1.6
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Comparison using errors
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Comparison using graph
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Using the model to make predictions
N 1507e0.0704t
Exponential model
N 1507e0.0704 16
t 16
Prediction for 2010
1507e1.1264
N 4648
The model predicts that about 4650 thousand cars
with engine sizes of 2 litres or more will be
registered in 2010.
Why might this not occur in practice?