Investigating y=b^x

In this lesson, we worked with exponential graphs and equations. While we were changing the values of b on the graphs, we needed to ask ourselves questions like “does the line get steeper quicker by increasing b?”, “why does the line never pass the x-axis?” and “why does the line decrease when the multiplier is a decimal?”. The answers to those are yes, the line gets steeper as the b increases because there is a higher number to be multiplied to, the line never passes the x-axis because the number is only being reduced to a smaller number and getting closer to 0 but not touching it, and the line simply decrease when the multiplier is a decimal because the number is not being multiplied buy a whole so it keeps being reduced.

Multiple Representations Web for Exponential Functions

You can relate an equation with a table, graph, and a situation. It goes the same for the rest of them. They are all connected if they all have the same pattern. For example, on a table, if your starting value is 20 and your y-values keep multiplying by three, then you’re equation is y=20•3^x. With the equation, you can make a graph. You can also make a situation out of what your numbers are. In the end situations, equations, graphs, and tables are all related.

Graph → Equation for Exponential Functions

Making an equation by using a graph is simple. First all you have do is find the y-intercept (the number that hits the y-axis when x=0) and put that number in the equation y=b•m^x as “b”. Next to find “m”, you divide the y value for x=1 by the y-intercept. Just to double check, you can do this with the values of x=2 and x=1, x=3 and x=2, and so on. You put the multiplier in as “m” into your equation and then you have your y=b•m^x equation. This all only works if you know the graph is exponential.

Important Ideas about Exponential Functions

Some of the basic facts someone should know is that although they both have a pattern, exponential is not like linear. They grow differently. Exponential graphs are curved. Exponential equations are written as y=b•m^x. Tables are increasing by 1 on the table for x and multiplied by your multiplier for the y.