Linear Function Lab Report

I believe that students should be able to recognize from a table of inputs/outputs that there is a trend connecting the numbers. If this trend goes up continuously by the same number, it would be said to be a linear function. Common examples of linear function would be distance traveled over time for objects traveling at constant speed; cost of gas in relation to gallons used. Certain situations are linear or not based on whether or not the rate of change is constant or varies. Linear systems are represented by f(x) = mx + b; the slope (m) and the y-intercept (b). In a table that represents a linear function, the input and out puts will be a set of solutions that will for a straight line. In a typical linear function, the m or slope determines the incline or decline of the line. The b determines the point where the line will cross or …show more content…
Exponential functions model situations where change is proportional to quantity. These functions have a consistent fixed period over which the function will double, triple, or quadruple as moves across the x-axis. With this function, there are typically two main equations used, exponential growth and decay; growth is y= a(1+ r)^x and decay is y= a(1-r)^x. a is the initial amount before the growth or decay, r is the growth or decay rate, and x is the number of time intervals that have passed. A real life example using exponential functions could be used when trying to determine the rate of bacteria growth over a period of time. The rate of change increases over time at a faster rate in exponential growth, and exponential decay has a rate that decreases over time. In an exponential function, the rate of change is note constantly changing at the same rate across the entire graph, therefore the graph is not a straight line. When plugging in values into a table, as the x values increase at a constant rate, the y values are increasing