Mathematics: Applications and Interpretation · Topic 2: Functions

AHL2.9 — Further modelling functions

Mathematics: Applications and Interpretation · SL / HL · syllabus-mapped notes

1. AIAHL2.9.1

   Exponential (half-life) and natural logarithmic models

   Using exponential decay to find half-life, and modelling with $f(x)=a+b\ln x$.

2. AIAHL2.9.2

   Sinusoidal models

   $f(x)=a\sin\!\big(b(x-c)\big)+d$: amplitude, period $\tfrac{2\pi}{b}$, phase shift $c$ and principal axis $d$.

3. AIAHL2.9.3

   Logistic models

   $f(x)=\dfrac{L}{1+Ce^{-kx}}$ models restricted growth with carrying capacity $L$.

4. AIAHL2.9.4

   Piecewise models

   Functions defined by different rules on different intervals; finding parameters for continuity.