Question

an archaeologist in turkey discovers a spear head that contains 80% of its original amount of C-14. Find the age of the spear head to the nearest year.

Answer 1

Hi!

As you know, the other person is very much incorrect, but I am here to help!

I have researched about original amounts of c-14, and know that it is very confusing and hard.

I am also currently taking this course, so I understand that it is frustrating.

The answer here is:

1847 years

Thank you!

God bless!

Good day/night!

Answer 2

The age of the spear head to the nearest year is 1845 years

Explanation:

We know that

half life time of C-14 is 5730 years

so, h=5730

we can use formula

`P(t)=P_0((1)/(2))^{(t)/(h) }`

now, we can plug value

`P(t)=P_0((1)/(2))^{(t)/(5730) }`

an archaeologist in turkey discovers a spear head that contains 80% of its original amount of C-14

so,

`P(t)=0.80P_0`

we can plug it

`0.80P_0=P_0((1)/(2))^{(t)/(5730) }`

now, we can solve for t

`0.80=((1)/(2))^{(t)/(5730) }`

`\ln \left(0.8\right)=\ln \left(\left((1)/(2)\right)^{(t)/(5730)}\right)`

`t=-(5730\ln \left(0.8\right))/(\ln \left(2\right))`

`t=1844.647`

So,

The age of the spear head to the nearest year is 1845 years