The family below is a square root function. Based on the graph, we can see that it has an initial rise and then falls back down to zero. The graph has a single peak, and it also decreases at a constant rate. This family is an exponential function. The equation for this type of curve is: ƒ(x)=ax^x+b*0 where x represents the input variable (time) and y values represent output variables (ozone in parts per million). This is one of the most common types of functions seen in nature because natural systems tend to grow exponentially as time goes on, such as population growth or oil production rates. The family below resembles that of an asymmetrical parabolic function which can be described by f(x)=k/cosh((a-ft)) As you can see from the graph, there are two peaks with a valley in the middle of each. The equation for this family is: ƒ(x)=k/(cosh((a-ft)) and x represents t (time) with y values representing output variables (ozone in parts per million) The family below resembles that of an even parabolic function which can be described by f(x)=k*tanh((ax)/b)) As you can see from the graph, there are two peaks with a valley in between them. This type of function has many implications as it relates to economics because it oscillates around its mean at a decreasing amplitude over time until reaching equilibrium, such as population growth rates or inflation rates. This family belongs to none other than a sinus