Question

Carbon-14 is an element which loses exactly half of its mass every 5730 years. The mass of a sample of carbon-

14 can be modeled by a function, M, which depends on its age, t (in years).
We measure that the initial mass of a sample of carbon-14 is 741 grams.
Write a function that models the mass of the carbon-14 sample remaining t years since the initial
measurement.

Answer 1

P = 741 * 0.5 ^ (t/5730)

Explanation:

If the Carbon-14 loses 50% of its mass for every 5730 years, we can write an exponencial equation as follows:

P = Po * (1-0.5)^t

Where t is the number of periods of 5730 years.

As we want periods of one year, we divide the time in the exponencial formula by 5730, so we have that:

P = Po * (1 - 0.5)^(t/5730)

Our inicial value is 741 grams, so that's the value of Po, so we have that:

P = 741 * 0.5 ^ (t/5730)