Certainly! Let's go through each part of the question step-by-step:
### 1.2.1 Name the type of dating that is illustrated in this table.
Answer: The type of dating illustrated in this table is Carbon Dating.
### 1.2.2 What is the half-life of carbon-14?
Answer: The half-life of carbon-14 is 5720 years.
### 1.2.3 Identify the following in the table: the dependent variable.
Answer: The dependent variable in the table is the percentage of original carbon remaining.
### 1.2.4 Calculate the value of:
(a) [tex]\( X \)[/tex]
To find [tex]\( X \)[/tex], we need to determine the number of years for 4 half-lives of carbon-14. Since the half-life of carbon-14 is 5720 years:
[tex]\[ X = \text{half-life of carbon-14} \times 4 \][/tex]
[tex]\[ X = 5720 \text{ years} \times 4 = 22880 \text{ years} \][/tex]
Answer: [tex]\( X = 22880 \text{ years} \)[/tex]
(b) [tex]\( Y \)[/tex]
To find [tex]\( Y \)[/tex], we need to calculate the percentage of original carbon remaining after 4 half-lives. The formula to use is:
[tex]\[ Y = \left( \frac{1}{2} \right)^4 \times 100\% \][/tex]
[tex]\[ Y = \left( \frac{1}{2} \right)^4 \times 100\% = \frac{1}{16} \times 100\% = 6.25\% \][/tex]
Answer: [tex]\( Y = 6.25\% \)[/tex]
### 1.2.5 What percentage of nitrogen-14 would you expect in a rock that is 11440 years old?
To find the percentage of nitrogen-14, we need to determine the percentage of carbon-14 remaining after 11440 years and then calculate the complement to 100%. From the table, we see that at 11440 years (2 half-lives), 25% of the original carbon-14 remains.
[tex]\[ \text{Percentage of nitrogen-14} = 100\% - \text{Percentage of carbon-14 remaining} \][/tex]
[tex]\[ \text{Percentage of nitrogen-14} = 100\% - 25\% = 75\% \][/tex]
Answer: The percentage of nitrogen-14 in a rock that is 11440 years old is 75%.
### 1.2.6 Explain why the carbon-14 dating method would not be suitable to date fossils over 80 million years old.
Answer:
The Carbon-14 dating method is not suitable for dating fossils over 80 million years old because the half-life of carbon-14 is only 5720 years. After about 50,000 years, the remaining amount of carbon-14 is so minuscule that it becomes challenging to measure accurately. Beyond a certain point, virtually no carbon-14 would be detectable, making the method ineffective for dating such ancient fossils.
