1. Population growth model: In demography, exponential function is usually used to describe population growth. Assuming that the population growth rate of a region is constant, the population of this region can be expressed by an exponential function. For example, if the initial population of a region is P0 and the annual growth rate is R, then after t years, the population of this region can be expressed as P = P0 * E (RT).
2. Radioactive decay model: In physics, radioactive decay is a common phenomenon, which can be described by exponential function. Assuming that the initial amount of a radioactive substance is N0 and the annual decay rate is r, the amount of this substance can be expressed as n = n0 * e (-rt) after t years.
3. Microbial growth model: In microbiology, microbial growth can also be described by exponential function. Assuming that the initial number of microorganisms is N0 and the daily growth rate is r, after t days, the number of microorganisms can be expressed as n = n0 * e (rt).
4. Compound interest model: In finance, compound interest is a common investment method, which can be described by exponential function. Assuming that an investor's initial investment is P0 and the annual interest rate is R, then after t years, the investor's total investment can be expressed as P = P0 * E (RT).
5. Drug metabolism model: In pharmacology, the metabolic process of drugs in vivo can also be described by exponential function. Assuming that the initial concentration of a drug is C0 and the metabolic rate per hour is R, the concentration of this drug can be expressed as c = C0 * E (-RT) after t hours.
These are just some examples. In fact, exponential function is also widely used in many other fields. Generally speaking, any system involving growth, decline, diffusion and other processes can be modeled by exponential function.