Question

Part 1

You will need to measure five different people. Record your measurements on a piece of paper. Using a tape measure or ruler, measure the length (in inches) of a person’s left foot and then measure the length (in inches) of that same person’s forearm (between their wrist and elbow). Refer to the diagrams below. You will have two measurements for each person.

(An easy way to measure the length of a foot is to have your subject stand on a piece of paper. Then, trace their foot and measure the outline once they move off the paper.)

To measure the forearm, measure inside the arm, between the wrist and the elbow.




Part 2
Organize your data and find the rate of change.

Create a table of the measurements for your data. Label the forearm measurements as your input and the foot measurements as your output.

Select two sets of points and find the rate of change for your data.

Describe your results. If you had to express this relation as a verbal statement, how would you describe it?
Part 3
Compare rates of change.

The equation below can be used to find the length of a foot or forearm when you know one or the other.

(length of the foot) = 0.860 • (length of the forearm) + 3.302

If you let y = length of the foot and x = length of the forearm, this equation can be simplified to
y = 0.860x + 3.302.

Using this equation, how long would the foot of a person be if his forearm was 17 inches long?

What is the rate of change of the equation from Part A?

Compare the equation from Part A to your data. Are they the same? Which has a greater rate of change? Why do you think the values are different?

Is the relation in your data a function? Why or why not? Could the equation in Part A represent a function? Why or why not? Explain your answer.
For this option you will submit the details from all three parts. Submit your measurements, the table, and description that you created in Parts 1 and 2. Submit your answers to the questions from Part 3.

Answer 1

You will likely need to actually measure a few people for parts 1 and 2, but the statement in part 2 should be something like "The length of the forearm of one person will be very similar to the length of their foot" or "As the length of the forearm increases, the length of the foot will increase in similar amounts".

Since the equation in pt.3 is y = 0.860x + 3.302, if x=17, then 0.860(17) + 3.302=17.922

The next question is dependant on pt.1

The data from pt.1 should be somewhat similar to the data you collected, the values between them are different because of the allowed error margin between the two.

The data can be made into a function using the "line of best fit". The equation in part A represents a function because there are no two points where two y coordinates are on the exact same x coordinate.