Question

A student in Greece discovers a pottery bowl

Answer 1

Answer:

The age of the pottery bowl to the nearest year is 15606 years.

Step-by-step explanation:

Let the initial amount of C-14 in the bowl i.e. $N_{0} = 100$ and today (say after t years) the amount of C-14 in the bowl i.e. N = 21.

Therefore, from the given equation we can write  

$21 = 100 e^{- 0.0001t}$ {Since, k is give to be 0.0001}

⇒ $0.21 = e^{- 0.0001t}$

Now, taking ln on both sides we get

ln 0.21 = - 0.0001t (ln e) {Since, $\ln a^{b} = b \ln a$}

⇒ - 1.560647 = - 0.0001t  {We have ln e = 1}

⇒ t = 15606.47 years ≈ 15606 years  

Therefore, the age of the pottery bowl to the nearest year is 15606 years.(Answer)