Introduction to Functions Discussion
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1. Describe a situation that models a linear pattern and then describe a situation that models a nonlinear pattern.
A situation that models a linear pattern could be tracking the number of hours a person works and the amount of money they earn. As the number of hours worked increases, the amount of money earned also increases at a constant rate. This can be represented by a linear function, where the dependent variable (money earned) is directly proportional to the independent variable (hours worked).
On the other hand, a situation that models a nonlinear pattern could be tracking the growth of a population of bacteria over time. Initially, the population could start growing slowly, but as time goes on and the resources available become more limited, the growth rate accelerates and the population increases exponentially. This can be represented by a nonlinear function, where the rate of growth is not constant and depends on the current population size.