Describe a situation that models a linear pattern and then describe a situation that models a nonlinear pattern.
Situation 1 (Linear pattern):
Consider a scenario where a company produces smartphones and their sales steadily increase over time. Let's assume that in the first month they sell 100 units, in the second month 200 units, and in the third month 300 units, and so on. This situation demonstrates a linear pattern because the sales are increasing by a fixed amount each month. The relationship between the number of months and the number of units sold can be represented by the equation y = 100x, where y is the number of units sold and x is the number of months.
Situation 2 (Nonlinear pattern):
Imagine a situation where you are filling a bathtub with water. Initially, when you turn on the faucet, the water level rises slowly. However, as the tub fills up, the water level increases at a faster rate. This scenario represents a nonlinear pattern because the relationship between the amount of water and the time it takes to fill the tub is not constant. Initially, it may take 10 minutes to fill the tub to half, but it might take another 15 minutes to fill the tub completely. The relationship between the time and the water level in the bathtub does not follow a straight line and cannot be represented by a simple equation.