Exponential Relationship
I am going to show an exponential relationship in 3 ways a graph, table, and equation. The relationship that im going to show is how every day a bike rider increases his miles by doubling the one before.
Exponential Table
![Picture](/uploads/5/9/7/0/59700795/1450642501.png)
This is my exponential table. It is exponential because my table starts at 0 and is constantly multiplying by 2 or doubling. The table is also showing that its exponential because its not decreasing like inverse and its not a straight line like linear but it is going up by a constant rate.
Exponential Graph
![Picture](/uploads/5/9/7/0/59700795/1450030879.png?250)
This is my exponential graph. It is exponential because it is doubling everyday the bike rider rides. My graph is exponential because it is increasing and it is doubling the miles from the day before to the next day so the bike rider is doubling his distance every day. It also starts at the x-axis and is increasing exponentially until the 7th day and he rides 64 miles the 7th day.
Exponential Equation
![Picture](/uploads/5/9/7/0/59700795/1450055966.png?250)
This is my exponential equation. This equation relates with my graph and table that I made also because it still uses doubling the miles per day in it. Exponential relationships are the equation y=a(b)^x. The dependent variable is the X and the a is the initial value and b is the growth value.
Parent Problem
![Picture](/uploads/5/9/7/0/59700795/1450641880.png?250)
A bike rider is training for a race. the bike rider is increasing his miles exponentially each day. Finish the table and say if the table is doubling, tripling, quadrupling etc.. Make an equation of the table.
Equation
My Mom got the exponential table really easy and had no problem with it. My mom did have some problems on the equation though. She didn't remember Y=a(b)^x but after I gave her the hint she got it right away.
Reflection
I learned a lot about the exponential Relationship in this investigation. I learned what exponential graphs, equations, and tables look like. I also learned how to make an equation with an exponential graph or table. I still have some trouble when I'm making my equation but I can make my table and graph now that I have learned how to.
Photo used under Creative Commons from Keith Allison