Carbon Dating QuarkNet, a Project Funded by the National Science

question 10

Essay

Carbon dating QuarkNet, a project funded by the National Science Foundation and the
U.S. Department of Energy, poses the following problem on its website:
"Last year, deep within the Soudan mine, QuarkNet teachers began a long-term
experiment to measure the amount of carbon-14 remaining in an initial 100-gram sample
at 2000-year intervals. The experiment will be complete in the year 32001. Fortunately, a
method for sending information backwards in time will be discovered in the year 29998,
so, although the experiment is far from over, the results are in."
Here is a portion of the data: $$\begin{array}{l}\begin{array} { l | c | c | c | c | c | c | c | c | c | c } \text { Time (yr) } & 0 & 2000 & 4000 & 6000 & 8000 & 10,000 & 12,000 & 14,000 & 16,000 & 18,000 \\\hline \text { Mass (g) } & 100 & 76 & 61 & 47 & 36 & 29 & 22 & 17 & 13 & 10\end{array}\\\text { A scatterplot of these data looks like: }\end{array}$$


a. Straighten the scatterplot by re-expressing these data and create an appropriate model
for predicting the mass from the year.
b. Use your model to estimate what the mass will be after 7500 years.
c. Can you use your model to predict when 50 g of the sample will be left? Explain.

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Definitions:

Production

The process of combining various inputs like labor, capital, and raw materials to make goods or provide services.

Proprietor's Income

The income earned by the owner of a sole proprietorship from the business.

Restaurant

A business establishment where meals or refreshments can be purchased and consumed by patrons.

Luigi

A fictional character in the Mario video game franchise, created by Nintendo, known as Mario's brother.