IB DP Maths: AI HL复习笔记2.6.2 Natural Logarithmic Models
Natural Logarithmic Models
What are the parameters of natural logarithmic models?
The a represents the value of the function when x = 1- The b determines the rate of change of the function
- A bigger absolute value of b leads to a faster rate of change
What can be modelled as a natural logarithmic model?
- A natural logarithmic model can be used when the variable increases rapidly for a period followed by a much slower rate of increase with no limiting value
- M(I) is the magnitude of an earthquake with an intensity of I
- d(I) is the decibels measured of a noise with an intensity of I
What are possible limitations a natural logarithmic model?
- A natural logarithmic graph is unbounded
- However in real-life the variable might have a limiting value
Worked Example
b)Find the sound intensity, in Wm-2, of a car alarm that has a sound intensity level of 105 dB.
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