Carbon-14 Dating.
Only 10% of the carbon-14 in a samll wooden bowl remains. How old is the bowl?
Half life of carbon is 5700 years.
.1 = .5^(t/5700)
t/5700 = log .1/log .5
t = 18935
18936 years
To determine the age of the wooden bowl using carbon-14 dating, we need to consider the concept of radioactive decay. Carbon-14 is an isotope of carbon that undergoes radioactive decay over time.
The half-life of carbon-14 is 5700 years, which means that after 5700 years, half of the original amount of carbon-14 will have decayed. In this case, we are given that only 10% of the carbon-14 remains, which means that 90% of the original carbon-14 has decayed.
To find the age of the bowl, we can set up an equation using the decay of carbon-14:
Remaining amount of carbon-14 = Original amount of carbon-14 * (1/2)^(number of half-lives)
We can substitute the given information into the equation:
0.1 = 1 * (1/2)^(number of half-lives)
Solving for the number of half-lives:
(1/2)^(number of half-lives) = 0.1
Taking the logarithm of both sides, we can solve for the number of half-lives:
log((1/2)^(number of half-lives)) = log(0.1)
Using the power rule of logarithms, we can bring down the exponent:
number of half-lives * log(1/2) = log(0.1)
Dividing both sides by log(1/2):
number of half-lives = log(0.1) / log(1/2)
Using a logarithmic calculator, we can find that log(0.1) = -1 and log(1/2) = -0.3010.
Plugging the values into the equation:
number of half-lives = -1 / -0.3010
This will give us the number of half-lives that have occurred. To find the age of the wooden bowl, we multiply the number of half-lives by the half-life of carbon-14:
age = number of half-lives * half-life of carbon-14
age = (number of half-lives) * 5700 years
Now, you can plug in the value for the number of half-lives and calculate the age of the bowl.