The five most common types of mathematical models involving exponential functions and logarithmic functions are:

• Exponential growth model: $$ y = a e^{bx}, \quad b>0$$
• Exponential decay model: $$ y = a e^{-bx}, \quad b>0$$
• Gaussian model: $$ y = a e^{-(x-b)^2/c}$$
• Logistic growth model: $$ y = \frac{a}{1+b e^{-rx}}$$
• Logarithmic models: $$ y = a+b \ln x, \quad y = a + b \log x$$