Many different situations in our everyday life can be broken down with numbers, and within those numbers patterns and trends begin to emerge. If we can understand the patterns that do emerge this helps us to make predictions that can make our lives that much easier.
Typically in high school Algebra 1 and 2, three major patterns of numbers are discussed in great detail. Linear, quadratic and exponential models can represent a wide variety of situations. All of these patterns can be further analyzed more efficiently using any Texas Instruments graphing calculator, no matter the model you are using. Any situation that involves data sets that contain gradual, constant changes usually falls within the linear family of functions. If the dependent variable grows or decays at a constant rate, this can be defined as the rate of change of the linear function. The growth of a plant or the hourly wages of an employee are excellent examples of linear sets of data. Standard form is y = mx + b.
A quadratic model is best used when data sets hit a peak or valley and then begin to rise and fall once again. For example, a car’s gas mileage as its speed fluctuates perfectly models a type of quadratic model. The gas mileage of a car typically improves as the miles per hour increase until about the 55 mph mark which at this point the gas mileage begins to drop again. Standard form is y = ax^2 + bx + c.
Finally, there is the exponential model. When data values grow or decay at a continuously quicker rate this means something is growing exponentially. The world’s population is a perfect example. Our population started growing at a fairly slow rate but steadily increased its rate over time until the last 25 years where populations have begun to absolutely explode. Standard form is y = a*b^x.
If you can create a model of a situation using the correct form, the trend model can be an extremely powerful mathematical tool. Graphing utilities can often provide you with a way of coming up with a trend equation with extremely complicated data sets. Texas Instruments has the best products for these modeling purposes we have discussed in this article.