Question

An archaeologist in Turkey discovers a spearhead that contains 23% of its original amount of C-14. Using the formula N = N0e^(-kt), where N0 is the initial amount of C-14 (at time t=0), N is the amount of C-14 at time t, k is 0.0001, and t is time in years, find the age of the spearhead to the nearest year.

a) 1170 years
b) 2340 years
c) 4680 years
d) 9360 years

Answer 1

The age of the spearhead is approximately 9360 years.

Step-by-step explanation:

To find the age of the spearhead, we can use the formula N = N0e^(-kt), where N is the amount of C-14 at time t, N0 is the initial amount of C-14, k is the decay constant (0.0001), and t is the time in years. We are given that the spearhead contains 23% of its original amount of C-14, so N = 0.23N0. Substituting these values into the formula, we have 0.23N0 = N0e^(-0.0001t). We can simplify this equation to e^(-0.0001t) = 0.23. Taking the natural logarithm of both sides, we have -0.0001t = ln(0.23). Solving for t, we find t ≈ 9360 years. Therefore, the age of the spearhead to the nearest year is option d) 9360 years.