3.5 | Exponential and Logarithmic Models


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: $$ y = a+b \ln x, \quad y = a + b \log x$$

E 3.5 Exercises