1. Describe a situation that models a linear pattern and then describe a situation that models a nonlinear pattern.
1. Linear pattern: A retail store sells t-shirts for $10 each. The number of t-shirts sold each day is directly proportional to the price. So, if 10 t-shirts are sold one day, 20 t-shirts will be sold the next day, and so on. This situation models a linear pattern because the increase in the number of t-shirts sold is consistent and can be represented by a straight line when plotted on a graph.
2. Nonlinear pattern: A car accelerates from 0 to 60 mph in different amounts of time depending on the amount of pressure applied to the gas pedal. At low pressure, it may take 10 seconds to reach 60 mph, but at higher pressure, it may only take 5 seconds. As the pressure increases, the time taken to reach 60 mph decreases at a decreasing rate. In this situation, the relationship between pressure and time taken to reach 60 mph does not follow a straight line and therefore, models a nonlinear pattern.