Question

A fossilized leaf contains 15% of its normal amount of carbon 14. How old is the fossil (to the nearest year)? Use 5600 years as the half-life of carbon 14. Solve the problem.
A. 35,828
B. 15,299
C. 1311
D. 21,839

Answer 1

I had this same question. The answer is b. 15,299.
hope this helps.

Answer 2

Answer:

Option B - 15299

Step-by-step explanation:

Given : A fossilized leaf contains 15% of its normal amount of carbon 14. Use 5600 years as the half-life of carbon 14.

To find : How old is the fossil (to the nearest year)?

Solution :

Let the normal or initial amount of carbon be A,

According to the question,

An exponential function form $f(t)=ab^t$

Where, a is the initial i.e, a=A

A fossilized leaf contains 15% of its normal amount of carbon 14.

So, f(t)=15% of A

i.e, $f(t)=0.15A$

b is half-life of Carbon-14 b=0.5

and t is the time span or age of the fossil in years.

Substitute all the values in the formula,

$0.15A=A(0.5)^t$

$\frac{0.15A}{A}=(0.5)^t$

$0.15=(0.5)^t$

Taking log both side,

$\log(0.15)=t\log(0.5)$

$t=\frac{\log(0.15)}{\log(0.5)}$

$t=2.73$

For 5600 years the age of the fossil is $t=2.73\times 5600=15288$

Therefore, Approximately Option B is correct.

The fossils are 15299 years old.