In Unit 3, we are investigating linear and exponential functions. In this discussion you will use an exponential function to design a guitar. For this discussion, you will post at least twice - 1) an initial post, and then 2) a reply to a classmate. The spacing of the frets on the neck of a classical guitar is determined from the equation d=(21.9)(2)(20−x)12/, where x = the fret number and d = the distance in centimeters to the x-th fret from the bridge. For your initial post: Answer the following 2 questions: 1. Determine the distance from the bridge for three consecutive frets. Round each answer to 3 decimal place. For example, you can calculate the distance from the bridge for the 4th, 5th and 6th fret. 2. Create the ratios of the highest fret to the previous fret and simplify to a decimal. Create the ratio of the next highest fret to the previous fret and simplify to a decimal. What are the values? For example, if your calculated the distance to the 4th, 5th and 6th fret, you would create the two ratios: 6th fret distance/5th fret distance, and 5th fret distance/4th fret distance. How are these ratios two related? Does this remind you of something we studied earlier in the course?
In Unit 3, we are investigating linear and exponential functions. In this discussion you will use an exponential function to design a guitar. For this discussion, you will post at least twice - 1) an initial post, and then 2) a reply to a classmate.
The spacing of the frets on the neck of a classical guitar is determined from the equation d=(21.9)(2)(20−x)12/, where x = the fret number and d = the distance in centimeters to the x-th fret from the bridge.
For your initial post: Answer the following 2 questions:
1. Determine the distance from the bridge for three consecutive frets. Round each answer to 3 decimal place. For example, you can calculate the distance from the bridge for the 4th, 5th and 6th fret.
2. Create the ratios of the highest fret to the previous fret and simplify to a decimal. Create the ratio of the next highest fret to the previous fret and simplify to a decimal. What are the values? For example, if your calculated the distance to the 4th, 5th and 6th fret, you would create the two ratios: 6th fret distance/5th fret distance, and 5th fret distance/4th fret distance. How are these ratios two related? Does this remind you of something we studied earlier in the course?
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