Question

A student in Greece discovers a pottery bowl that contains 28% of its original amount of C-14 find the age of the pottery bowl to the nearest year

Answer 1

Answer:

The age of the pottery bowl is 10523 years.

Step-by-step explanation:

Amount of substance:

The amount of a substance after t years is given by the following equation:

$A(t) = A(0)(1-r)^t$

In which A(0) is the initial amount and r is the decay rate.

Half-life of C14.

Researching, the half-life of c-14 is 5730 years.

This means that:

$A(5730) = 0.5A(0)$

We use this to find r. So

$A(t) = A(0)(1-r)^t$

$0.5A(0) = A(0)(1-r)^{5730}$

$(1-r)^{5730} = 0.5$

$\sqrt[5730]{(1-r)^{5730}} = \sqrt[5730]{0.5}$

$1 - r = 0.5^{\frac{1}{5730}}$

$1 - r = 0.99987903922$

So

$A(t) = A(0)(0.99987903922)^t$

Age of the pottery bowl:

We have that:

$A(t) = 0.28A(0)$

We have to find t. So

$A(t) = A(0)(0.99987903922)^t$

$0.28A(0) = A(0)(0.99987903922)^t$

$(0.99987903922)^t = 0.28$

$\log{(0.99987903922)^t} = \log{0.28}$

$t\log{0.99987903922} = \log{0.28}$

$t = \frac{\log{0.28}}{\log{0.99987903922}}$

$t = 10523.1$

So

The age of the pottery bowl is 10523 years.