Graphs on Semi-Log Graph Paper

What is the difference between a semi-log graph and a rectangular graph? First off, a semi-log graph is meant to graph exponential functions. A semi-log graph is meant to be used for exponential growth functions. A rectangular graph is used only for regular functions or for non-exponential functions. The semi-log graph is useful because it is the most efficient way to demonstrate an exponential function where the exponent is unknown on a graph. A disadvantage to this is that a rectangular graph allows more accurate functions to be seen. A graph with a logarithmic graph scale can be misleading because most people who would see a straight line on a semi-log graph would assume that the function was a normal function without knowing the function is an exponential growth function.

Exponential Functions

Exponential Functions are quite frankly not emphasized in society for how impactful it can be. An exponential function is a function in which the value is raised by the power of the number. For example, f(x)=3 to the x power, is an exponential function. Here's another example that exponential functions can be represented in quite a fiction way. Every time someone yawns, 5 more people yawn in response, this problem happens in the span of eight seconds. If x equals the amount of seconds and y equals the people, it is clear that if you plugged in a large x-value, you would receive an extremely high y-value. For instance, once 100 second passes, 545,915,033 people are now yawning. Think of it like an unstoppable virus, it spreads rapidly and intensely fast. If this were to be represented in a graph, it would look like this.

The function can usually be expressed with the following equation. y=number^x. But what determines the graph to become thinner is how much higher the initial number is. Which function would look more like a straight line when graphed, y=10^x or y=100^x? The answer is y=100^x power as the first equation would be (10)(10) if the constant is in the power of two, but the second equation would be (100)(100). As it is evident, the outcome of an exponential function will most of the time produce a high number because of how intensely the number grows when x is changed.