35.5: Analysis

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Rolling the Cubes

Look at your data for the cubes. You will need to decide whether the number of throws or the number of cubes remaining is the independent variable. Determine a scale that will allow you to place data for all three colors onto a single graph. Use a different colored pencil for each of the different colors on the cubes. Graph your data for each list (red, black, and white). Include a sketched best fit line for each set of data.
Do the graphed sets of data indicate a constant or non-constant rate of decay? How do you know?
Determine and record the half-life, in units of throws, for each color (red, black, white), based on your data. This is the approximate number of throws it took to have half of the cubes remaining; this will be a whole number. Record your answers. Compare this information with your predicted half-life for each color. What could account for any differences between your predicted and actual half-life for each color?

Table \(\PageIndex{1}\)
Color	Actual Half-life (Number of Throws)
Red
Black
White

Dating the Beans

Assume the black beans are carbon-14 atoms and that each sample started with 32 black beans. Complete and document the decay process to track the fractional amount of black beans that would remain out of the original 32, after each decay, and follow the decay process until you have numbers that match your bean samples. Include the time that has passed at each half-life. The process is started below for you.

Table \(\PageIndex{2}\)
Amount	Fraction	Time
64	-	-
32	1/2	5730 years

Use the decay process for your black beans, and the half-life of carbon-14, to carbon date your fictitious samples.

Table \(\PageIndex{3}\): Age of Fictitious Samples
Sample	Age (Years)
1
2
3
4
5

Contributors and Attributions

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