Question

Find the age of a spearhead to the nearest year based on its C-14 content (27% of the original). Use the formula N = No * e^(kt),

a. 900 years
b. 950 years
c. 1,000 years
d. 1,050 years

Answer 1

To calculate the age of a spearhead based on 27% remaining C-14 content, we use the decay formula with the spearhead's current and original C-14 levels, alongside Carbon-14's half-life to determine the age. The correct option is b.

Step-by-step explanation:

To find the age of a spearhead based on its C-14 content, which is 27% of the original, we use the formula N = No * e(kt). Here, N is the current percentage of Carbon-14, No is the original percentage (100%), k is the decay constant, and t is the time in years.

The decay constant k can be found using the half-life formula k = -ln(2) / t1/2, where t1/2 is the half-life of Carbon-14, approximately 5730 years.

Rewriting the initial equation for t and substituting the given values:

ln(N/No) = kt
ln(0.27) = (-ln(2) / 5730) * t

Solving for t will give us the age of the spearhead. The correct option is b.