only 5% of the carbon-14 in a small wooden bowl remains , how old is the bowl?
Hint, half-life for carbon –14 us 5730 years
Since this is a "half-life" situation we can use
1/2 or .5 as the base in our exponential equation
5 = 100 (1/2)^(t/5730)
.05 = .5 ^(t/5730)
take ln of both sides
ln 0.05 = (t/5730) ln 0.5
t/5730 = ln 0.05/ln 0.5 = 4.3219...
t = appr 24765 years
Unless your teacher gives you 5700 as the half life.
To determine the age of the wooden bowl, we can use the concept of carbon-14 dating and its half-life.
The half-life of carbon-14 is the amount of time it takes for half of the carbon-14 atoms in a sample to decay. In the case of carbon-14, its half-life is 5730 years. This means that after 5730 years, half of the carbon-14 originally present in the sample will have decayed.
Since only 5% of the carbon-14 remains in the wooden bowl, we can deduce that 95% of it has decayed. This remaining 5% represents half of the original carbon-14 in the bowl.
To find the number of half-lives that have elapsed, we can use the formula:
Number of half-lives = Log(base 2) (Remaining carbon-14 / Original carbon-14)
By substituting the values, we get:
Number of half-lives = Log(base 2) (0.05 / 0.50)
Using a calculator to calculate the logarithm, we find that the number of half-lives is approximately 3.87.
Finally, to determine the age of the bowl, we multiply the number of half-lives by the half-life of carbon-14:
Age of the bowl = Number of half-lives × Half-life of carbon-14
Age of the bowl = 3.87 × 5730 years
The age of the wooden bowl is approximately 22,198.1 years.