Final answer:
A periodic function example is daily temperature, featuring regular intervals, amplitude, and phase shift, with the domain being time and the range being temperature variances. A logistic function example is yeast population growth, which includes initial exponential growth, slowing growth, and leveling-off at a carrying capacity, with the domain as non-negative time and the range from zero to the maximum population.
Step-by-step explanation:
A specific real-life example of a periodic function is the daily temperature throughout a year which follows a roughly sinusoidal pattern. For instance, in a particular region, temperatures may be highest in July and lowest in January each year. Some of the defining characteristics or features of a periodic function include:
- Repeating patterns at regular intervals (periodicity)
- Amplitude, which measures the height of the peaks and depth of the troughs from the middle
- Phase shift, which determines the horizontal shift of the function
For our model of daily temperature, the domain might be all real numbers representing time, while the range would be restricted to the minimum and maximum temperatures experienced over the course of a year.
An example of a logistic function is the population growth of yeast in a controlled environment. This growth can be characterized by:
- An initial period of exponential growth
- A slowing of growth as resources become limited
- A leveling-off as the population approaches the carrying capacity of the environment
The domain of this function is all non-negative real numbers (time can't be negative), and the range is between zero and the carrying capacity of the environment, reflecting the maximum population that can be sustained.