Question

A farmer in china discovers a mammal hide that contains 54% of its original amount of c-14. Find the age of the mammal hide to the nearest year

Answer 1

Answer:

6163.2 years

Step-by-step explanation:

The formula we use for evaluating the C 14 decay is

$A_t=A_0e^{-kt}$

Where

$A_t$=Amount of C 14 after “t” year

$A_0$= Initial Amount

t= No. of years

k=constant

In our problem we are given that $A_t$ is 54% that is if $A_0=1$ , $A_t=0.54$

Also , k=0.0001

We have to find t=?

Let us substitute these values in the formula

$0.54=1* e^{-0.0001t}$

Taking log on both sides to the base 10 we get

$log 0.54=log e^{-0.0001t}$

$-0.267606 = -0.0001t*log e$

$-0.267606 = -0.0001t*0.4342$

$t=\frac{-0.267606}{-0.0001*0.4342}$

$t=6163.20$

t=6163.20 years

Answer 2

the answer would be 6.16 or 6 years