Question

An archaeologist locates a fossil of an early human skeleton. To determine the age of the fossil, the archaeologist utilizes a


technique called carbon dating, where the relative amount of carbon-14 can help determine the age of the fossil. Carbon-14 has a


half-life of about 5700 years.


He finds that the fossil contains 15% of the amount of carbon-14 anticipated when compared to a living femur of the same size


The decay of carbon-14 can be calculated as shown below, where No is original amount of carbon-14, t is the time of decay, in


years, represents the rate of decay, and N(I) represents the amount of carbon-14 remaining.


N(t) = Noert


Rounded to the nearest year, the skeleton is approximately___ years old.

Answer 1

Answer:

15549 yrs old

Step-by-step explanation:

To find the decay constant r we use the formula

t1/2 = 0.693/r

t1/2 is the half-life 5700

5700 = 0.693/r

r = 0.693/5700 = 0.000122 per sec

For the 15% remaining from an initial value of 100%, time t is calculated from

N = Noe^(-rt)

0.15 = 1e^(-0.000122t)

we take natural log of both sides

Ln 0.15 = Ln e^(-0.000122t)

-1.897 = -0.000122t

t = -1.897/-0.000122 = 15549.18 yrs

Approximately 15549 yrs old