Carbon-14 decay (radiocarbon dating) is used in archaeology to measure
the age of ancient pottery. Carbon-14 has a half-life of 5830 years. How old is a
pot in which 20% of the Carbon-14 has decayed?
half-life ----> so I will use 1/2 as the base in my exponential equation
half-life is 5830, so I will use t/5830 as my exponent
amount = (1/2)^(t/5830) = .5^(t/5830)
20% has decayed ---> I have 80% or .8 left
.8 = .5^(t/5830)
take log of both sides and use log rules
(t/5830)log .5 = log .8
t/5830 = log.8/log.5
t = 5830log.8/log.5 = .....
You do the button pushing
To determine the age of the pottery in which 20% of the Carbon-14 has decayed, we can use the concept of half-life.
The half-life of Carbon-14 is 5830 years, which means that after 5830 years, half of the initial amount of Carbon-14 will have decayed.
To find out how many half-lives have passed to reach 20% decay, we can use the following formula:
(number of half-lives) = (log of remaining amount / log of 0.5)
Let's calculate the number of half-lives:
(number of half-lives) = log(0.20) / log(0.5) ≈ 2.73
Since the number of half-lives only represents the whole number of half-lives that have occurred, we can round this down to 2.
Now, we can find the age of the pottery by multiplying the number of half-lives by the half-life period:
(age of the pottery) = 2 * 5830 ≈ 11660 years
Therefore, the age of the pottery in which 20% of the Carbon-14 has decayed is approximately 11660 years.
To determine the age of a pot in which 20% of the Carbon-14 has decayed, we can use the concept of half-life. The half-life of Carbon-14 is given as 5830 years, which means that every 5830 years, half of the Carbon-14 atoms in a sample will decay.
Here's how you can calculate the age:
1. Start with the assumption that the initial amount of Carbon-14 in the pot was 100%. We can assign this value as the initial quantity (Q0).
2. Since 20% of the Carbon-14 has decayed, the remaining amount is 80%. We can assign this value as the final quantity (Qf).
3. The decayed portion of Carbon-14 is equal to the difference between the initial and final quantities: Qf = Q0 - (Decayed Portion).
4. To find the decayed portion, we need to calculate the number of half-lives that have occurred. Since each half-life is 5830 years, divide the percentage decay (20%) by 50% (one half-life) to determine the number of half-lives (n) that have occurred: n = (Percentage Decay) / 50.
In this case, n = 20 / 50 = 0.4 half-lives.
5. Now, we can use the half-life formula to calculate the decayed portion: Decayed Portion = Q0 * (1/2)^n.
Substitute the values: Decayed Portion = 100 * (1/2)^0.4.
6. Calculate the remaining amount of Carbon-14: Qf = Q0 - Decayed Portion = 100 - (100 * (1/2)^0.4).
7. Now, we need to find the age of the pot. Multiply the number of half-lives by the length of one half-life: Age = n * Half-life.
In this case, Age = 0.4 * 5830.
After performing these calculations, you will obtain an approximate age for the pot in which 20% of the Carbon-14 has decayed.