Answer:
28500 years
Explanation:
Applying,
A = A'([tex]2^{x/y}[/tex])............... Equation 1
Where A = Original mass of Carbon-14, A' = Final mass of carbon-14 after decaying, x = total time, y = half-life.
From the question,
Given: A = 1 g, A' = 31.3 mg = 0.0313 g, y = 5700 years.
Substitute these values into equation 1
1 = 0.0313([tex]2^{x/5700}[/tex])
[tex]2^{x/5700}[/tex] = 1/0.0313
[tex]2^{x/5700}[/tex] = 31.95
[tex]2^{x/5700}[/tex] ≈ 32
[tex]2^{x/5700}[/tex] ≈ 2⁵
Equating the base and solve for x
x/5700 ≈ 5
x ≈ 5×5700
x ≈ 28500 years
