. . . I had the same thought about the circular reasoning involved in estimating the age of the earth, and even told my teacher that it sounded absurd. She, being a faithful Christian, told me to write what the textbooks stated for the sake of the exam without arguing. My doubt now is this: The age of fossils is estimated based on Carbon Dating—measuring how much Carbon-14 is present, and using the halflife principle. How can we argue against such scientific procedures?  (Hannah’s first question)

I would rather point you to good online material, which are written by people who have a background in science, than give you an answer myself.

Scientists who are Christians tell us that Carbon Dating is a friend of Christians. This is because, even in the hands of scientists who do not believe in a young earth, Carbon Dating does not point to a millions-of-years-old earth but to one that is less than a million years old. However, even this is far bigger than the 6000 years we want to arrive at, based on the Holy Scriptures.

The problem lies in the assumptions made by scientists when using Carbon Dating. I am not suggesting that they are being dishonest. It is just that they assume that the environment on the earth has been fairly constant, whereas Christians have sufficient reason to believe that the earth’s atmosphere has changed in the last 6,000 years.

Do read the following articles about Carbon Dating.

Does carbon dating prove the Earth is millions of years old?
Carbon-14 dating – explained in everyday terms
Carbon Dating—Answers for kids
Doesn’t Carbon-14 Dating Disprove the Bible?

I would like to quote from the first article because the candle example is useful in understanding the framework of the argument (against the results obtained from Carbon Dating).

Although this technique looks good at first, carbon-14 dating rests on two simple assumptions. They are, obviously, assuming the amount of carbon-14 in the atmosphere has always been constant, and its rate of decay has always been constant. Neither of these assumptions is provable or reasonable.

An illustration may help:
Imagine you found a candle burning in a room, and you wanted to determine how long it was burning before you found it. You could measure the present height of the candle (say, seven inches) and the rate of burn (say, an inch per hour). In order to find the length of time since the candle was lit we would be forced to make some assumptions. We would, obviously, have to assume that the candle has always burned at the same rate, and assumes an initial height of the candle.

The answer changes based on the assumptions. Similarly, scientists do not know that the carbon-14 decay rate has been constant. They do not know that the amount of carbon-14 in the atmosphere is constant. Present testing shows the amount of C-14 in the atmosphere has been increasing since it was first measured in the 1950’s. This may be tied in to the declining strength of the magnetic field.