Describe a situation that models a linear pattern and then describe a situation that models a nonlinear pattern
Linear pattern:
A situation that models a linear pattern could be the relationship between the number of hours studied and the grade obtained in an exam. Let's say a student studies for 1 hour and gets a grade of 70, studies for 2 hours and gets a grade of 75, studies for 3 hours and gets a grade of 80, and so on. In this case, as the number of hours studied increases, the grade obtained also consistently increases at a constant rate. This linear pattern can be represented by the equation y = mx + b, where y represents the grade obtained, x represents the number of hours studied, m represents the rate of increase (slope), and b represents the initial grade obtained when no hours are studied (y-intercept).
Nonlinear pattern:
A situation that models a nonlinear pattern could be the relationship between the amount of fertilizer used and the growth of a plant. Let's say a gardener uses 1 pound of fertilizer and the plant grows by 2 inches, uses 2 pounds of fertilizer and the plant grows by 5 inches, uses 3 pounds of fertilizer and the plant grows by 10 inches, and so on. In this case, as the amount of fertilizer used increases, the growth of the plant does not follow a constant rate. The growth may accelerate or decelerate depending on the amount of fertilizer used. This nonlinear pattern cannot be represented by a simple linear equation. Instead, it may require a more complex mathematical model or function to accurately describe the relationship between fertilizer usage and plant growth.